Communications in Mathematical Analysis and Applications
type: channel
description: Communications in Mathematical Analysis and Applications (CMAA) publishes research papers relevant to mathematical analysis and its applications. CMAA publishes original research articles of high quality on a topic in Real and harmonic analysis, Complex analysis, Numerical analysis, Partial differential equations, Dynamical systems, Control and optimization, Probability, Mathematical biology, Statistics etc.
publisher: Global Science Press
language: en
publication name: Communications in Mathematical Analysis and Applications
issn: 2790-1920
items: Reflected BSDEs Driven by RCLL Martingales with Stochastic Lipschitz Coefficient in a General Filtration: Analysis and Applications
items: Classical Solutions to a Model for Heat Generation During Acoustic Wave Propagation in a Standard Linear Solid
items: $L^2$-Contraction and Asymptotic Stability of Large Shock for Scalar Viscous Conservation Laws
items: Normalized Ground State Solution to a Mixed Schrödinger System in a Plane
items: Corrigendum to: "On the Eigenvalue Problem for a Bulk/Surface Elliptic System"
items: Exponential Ergodicity for Time-Periodic McKean-Vlasov SDEs
items: Recent Progress on Stochastic Fractional Diffusion Equations with Space-Time White Noise
items: Strong Convergence of Functional Stochastic Differential Equations via the Functional Itô Calculus
items: A Stochastic Maximum Principle for Relaxed Control with General Risk Measure and Its Application in Finance
items: Long Time Behavior of the Stochastic 2D Navier-Stokes Equations
items: Smooth Densities of Stochastic Differential Equations Forced by Degenerate Stable Type Noises
items: Asymptotics in Wasserstein Distance for Empirical Measures of Markov Processes
items: Preface：Special Issue on Recent Progresses in Stochastic Differential Equations and Stochastic Partial Differential Equations
items: Crossing Thresholds in High Contrast Boundary Homogenization Problems: A Review
items: Variational Functionals for the Characterization of BV and Sobolev Spaces
items: Large Time Behavior of Solutions to Burgers Equation with a Time Delay
items: Multi-Level Structured Deformations: Relaxation via a Global Method Approach
items: Homogenization of an Elliptic System Involving Non-Local and Equi-Valued Interface Conditions
items: Uncertainty and Strichartz Type Inequalities for Fractional Hajłasz-Sobolev Spaces
items: On the Eigenvalue Problem for a Bulk/Surface Elliptic System
items: Preface: Proceedings of the International Conference on Elliptic and Parabolic Problems, Gaeta, Italy, 20-24 May 2024
items: Decay Structure of the Zener-Type Viscoelastic Plate with Type II Heat Conduction in the Whole Space
items: Suppression of Chemotactic Singularity via Poiseuille Flow in a Self-Consistent Patlak-Keller-Segel-Navier-Stokes System
items: Compact Embeddings and Pitt’s Property for Weighted Sequence Spaces of Sobolev Type
items: Localization and Multiplicity for Stationary Stokes Systems with Variable Viscosity
items: A Note on the Global Existence in a Fully Parabolic Patlak-Keller-Segel-Navier-Stokes System
items: Local Well-Posedness and Weak-Strong Uniqueness to the Incompressible Vlasov-MHD System
items: A Constructive Proof of Korn’s Scaled Inequalities for Shells
items: The Biot Stress-Right Stretch Relation for the Compressible Neo-Hooke-Ciarlet-Geymonat Model and Rivlin’s Cube Problem
items: Preface: Asymptotic Analysis and Elasticity Theory: A Collection of Papers Dedicated to Professor Philippe G. Ciarlet on the Occasion of His 85th Birthday

Reflected BSDEs Driven by RCLL Martingales with Stochastic Lipschitz Coefficient in a General Filtration: Analysis and Applications
type: item
description: In this paper, we investigate reflected backward stochastic differential equations with a single, discontinuous barrier, driven by a right-continuous, left-limited martingale within a general filtration. We establish the existence and uniqueness of solutions under a stochastic Lipschitz condition on the generator and a reflection process that is right-continuous with left limits. As an application, we use these results to determine fair pricing for American contingent claim options in a financial market driven by Azéma’s martingale, incorporating elements of asymmetric information.
subject: Articles
  topic: section
subject: Reflected BSDEs
  topic: keywords
subject: RCLL martingales
  topic: keywords
subject: stochastic Lipschitz coefficient
  topic: keywords
subject: Azéma's martingale market model
  topic: keywords
subject: American option
  topic: keywords
creator: Badr Elmansouri
creator: Mohamed El Otmani
rights: Copyright (c) 2026 Communications in Mathematical Analysis and Applications
date: 2026-02-25
publication date: 2026-02-25
starting page: 115
ending page: 153
doi: 10.4208/cmaa.2025-0025

Classical Solutions to a Model for Heat Generation During Acoustic Wave Propagation in a Standard Linear Solid
type: item
description: In an open bounded real interval, this manuscript studies the evolution system \begin{cases} u_{ttt}+\alpha u_{tt} = \big(\gamma(\Theta)u_{xt}\big)_x + \big(\hat{\gamma}(\Theta)u_x\big)_x, \\ \Theta_t = D\Theta_{xx} + \Gamma(\Theta)u_{xt}^2, \end{cases} which arises as a model for the generation of heat during propagation of acoustic waves in a standard linear solid. A statement in local existence and uniqueness of classical solutions is derived for arbitrary $D>0$ and $\alpha\ge0$, for sufficiently smooth $\gamma,\hat{\gamma}$ and $\Gamma$ with $\gamma>0,\hat{\gamma}>0$ and $\Gamma\ge0$ on $[0,\infty)$, and for all suitably regular initial data of arbitrary size.
subject: Articles
  topic: section
subject: Nonlinear acoustics
  topic: keywords
subject: thermoelasticity
  topic: keywords
subject: smooth solution
  topic: keywords
subject: standard linear solid
  topic: keywords
creator: Torben Fricke
creator: Michael Winkler
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2026-01-28
publication date: 2026-01-28
starting page: 91
ending page: 114
doi: 10.4208/cmaa.2025-0023

$L^2$-Contraction and Asymptotic Stability of Large Shock for Scalar Viscous Conservation Laws
type: item
description: We investigate $L^2$-contraction and time-asymptotic stability of large shock for scalar viscous conservation laws with polynomial flux. For the flux $f(u) = u^p (2 ≤ p ≤ 4)$ in the regime of its strict convexity, we can prove $L^2$-contraction and time-asymptotic stability of arbitrarily large viscous shock profile in $H^1$-framework by using a-contraction method with time-dependent shift and suitable weight function, which answers a question in [Blochas and Cheng, arXiv2501.01537, 2025]. Additionally, if the initial perturbation belongs to $L^1$ , then $L^2$ time-asymptotic decay rate $t^{−1/4}$ can be obtained.
subject: Articles
  topic: section
subject: $a$-contraction
  topic: keywords
subject: asymptotic stability
  topic: keywords
subject: large shock
  topic: keywords
creator: Alexis F. Vasseur
creator: Yi Wang
creator: Jian Zhang
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2026-01-15
publication date: 2026-01-15
starting page: 35
ending page: 64
doi: 10.4208/cmaa.2025-0021

Normalized Ground State Solution to a Mixed Schrödinger System in a Plane
type: item
description: In this paper, we establish the existence of positive ground state solutions for a class of mixed Schrödinger systems with concave-convex nonlinearities in $\mathbb{R}^2$, that is \begin{cases} -\partial_{xx}u + (-\Delta)_y^s u + \lambda_1 u = \mu_1 u^{p-1} + \beta r_1 u^{r_1-1}v^{r_2}, \\ -\partial_{xx}v + (-\Delta)_y^s v + \lambda_2 v = \mu_2 v^{q-1} + \beta r_2 u^{r_1}v^{r_2-1} \end{cases} subject to the $L^2$-norm constraints \begin{equation} \int_{\mathbb{R}^{2}} u^{2}dxdy = a, \qquad \int_{\mathbb{R}^{2}} v^{2}dxdy = b, \end{equation} where $(x,y)\in\mathbb{R}^2$, $u,v\geq0$, $s\in(1/2,1)$, $\mu_1,\mu_2,\beta>0$, $r_1,r_2>1$, the prescribed masses $a,b>0$, and the parameters $\lambda_1,\lambda_2$ appear as Lagrange multipliers. Moreover, the exponents $p,q,r_1+r_2$ satisfy $2(1+3s)/(1+s) < p,q,r_1+r_2 < 2_s$, where $2_s = 2(1+s)/(1-s)$. To obtain our main existence results, we employ variational techniques such as the mountain pass theorem, the Pohozaev manifold, Steiner rearrangement, and others, consolidating the works [Jeanjean et al., Nonlinear Differ. Equ. Appl. 31 (2024)].
subject: Articles
  topic: section
subject: Pohozaev identity
  topic: keywords
subject: mountain pass theorem
  topic: keywords
subject: normalized solution
  topic: keywords
subject: mixed Schrödinger system
  topic: keywords
creator: Ashutosh Dixit
creator: Amin Esfahani
creator: Hichem Hajaiej
creator: Tuhina Mukherjee
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2026-01-15
publication date: 2026-01-15
starting page: 1
ending page: 34
doi: 10.4208/cmaa.2025-0020

Corrigendum to: "On the Eigenvalue Problem for a Bulk/Surface Elliptic System"
type: item
description: This note corrects a mistake in the paper ”On the eigenvalue problem for a bulk/surface elliptic system” by the author, appeared in [Vitillaro, Commun. Math. Anal. Appl. 4 (2025)].
subject: Articles
  topic: section
subject: Bulk/surface
  topic: keywords
subject: elliptic system
  topic: keywords
subject: eigenvalue problem
  topic: keywords
subject: oscillation modes
  topic: keywords
subject: standing solutions
  topic: keywords
subject: hyperbolic dynamic boundary conditions
  topic: keywords
subject: wave equation
  topic: keywords
creator: Enzo Vitillaro
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2026-01-13
publication date: 2026-01-13
starting page: 154
ending page: 156
doi: 10.4208/cmaa.2025-0024

Exponential Ergodicity for Time-Periodic McKean-Vlasov SDEs
type: item
description: As extensions to the corresponding results derived for time homogeneous McKean-Vlasov SDEs, the exponential ergodicity is proved for time-periodic distribution dependent SDEs in three different situations: 1) in the quadratic Wasserstein distance and relative entropy for the dissipative case; 2) in the Wasserstein distance induced by a cost function for the partially dissipative case; and 3) in the weighted Wasserstein distance induced by a cost function and a Lyapunov function for the fully non-dissipative case. The main results are illustrated by time inhomogeneous granular media equations, and are extended to reflecting McKean-Vlasov SDEs in a convex domain.
subject: Articles
  topic: section
subject: Time-periodic McKean-Vlasov SDE
  topic: keywords
subject: exponential erodicity
  topic: keywords
subject: relative entropy
  topic: keywords
subject: Wasserstein distance
  topic: keywords
creator: Panpan Ren
creator: Karl-Theodor Sturm
creator: Feng-Yu Wang
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2026-01-13
publication date: 2026-01-13
starting page: 65
ending page: 90
doi: 10.4208/cmaa.2025-0022

Recent Progress on Stochastic Fractional Diffusion Equations with Space-Time White Noise
type: item
description: We review the recent development on stochastic fractional diffusion equations with space-time white noise. We explicate the Fox $H$-function, fundamental solutions, mild Skorohod solution and its properties including existence and uniqueness, intermittent property and Hölder continuity.
subject: Articles
  topic: section
subject: Stochastic partial differential equation
  topic: keywords
subject: space-time white noise
  topic: keywords
subject: Fox $H$-function
  topic: keywords
subject: intermittency
  topic: keywords
subject: Hölder continuity
  topic: keywords
creator: Yuhui Guo
creator: Jiang-Lun Wu
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2025-11-17
publication date: 2025-11-17
starting page: 626
ending page: 646
doi: 10.4208/cmaa.2025-0019

Strong Convergence of Functional Stochastic Differential Equations via the Functional Itô Calculus
type: item
description: In general, Malliavin calculus is exploited to construct the Milstein scheme for functional stochastic differential equations due to the appearance of anticipative stochastic integrals. In this paper, by passing the Malliavin calculus, Milstein-type schemes are constructed via the functional Itô calculus for a range of functional stochastic differential equations. As regards the Milstein schemes designed, the strong convergence with the rate 1 is established for functional stochastic differential equations, where the delay measure need not be absolutely continuous with respect to the Lebesgue measure.
subject: Articles
  topic: section
subject: Functional Itô calculus
  topic: keywords
subject: Milstein scheme
  topic: keywords
subject: functional stochastic differential equation
  topic: keywords
subject: convergence rate
  topic: keywords
subject: strong convergence
  topic: keywords
creator: Jianhai Bao
creator: Jiaqing Hao
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2025-11-17
publication date: 2025-11-17
starting page: 594
ending page: 625
doi: 10.4208/cmaa.2025-0018

A Stochastic Maximum Principle for Relaxed Control with General Risk Measure and Its Application in Finance
type: item
description: This paper deals with optimal relaxed control problem where the cost functional is a general risk measure instead of an expectation. We develop a stochastic maximum principle for this kind of optimal control problems using a variational method. Then, under the expectation optimization objective, a dynamic programming principle is studied and its connections to the adjoint process is shown. At last, the result is applied to two examples. One is a linear quadratic problem and the other is an optimal investment problem.
subject: Articles
  topic: section
subject: Measure valued control process
  topic: keywords
subject: stochastic maximum principle
  topic: keywords
creator: Shuaiqi Zhang
creator: Jie Xiong
creator: Xin Zhang
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2025-11-17
publication date: 2025-11-17
starting page: 577
ending page: 593
doi: 10.4208/cmaa.2025-0017

Long Time Behavior of the Stochastic 2D Navier-Stokes Equations
type: item
description: We review some basic results on existence and uniqueness of the invariant measure for the two-dimensional stochastic Navier-Stokes equations. A large part of the literature concerns the additive noise case; after revising these models, we consider our recent result [Ferrario and Zanella, Discrete Contin. Dyn. Syst. 44(1), 2024] with a multiplicative noise.
subject: Articles
  topic: section
subject: Two dimensional stochastic Navier-Stokes equations
  topic: keywords
subject: invariant measure
  topic: keywords
subject: multiplicative noise
  topic: keywords
subject: degenerate noise
  topic: keywords
creator: Benedetta Ferrario
creator: Margherita Zanella
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2025-11-17
publication date: 2025-11-17
starting page: 550
ending page: 576
doi: 10.4208/cmaa.2025-0016

Smooth Densities of Stochastic Differential Equations Forced by Degenerate Stable Type Noises
type: item
description: Malliavin calculus for stochastic differential equations (SDEs) forced by degenerate stable like noises has been intensively studied recently, see e.g. [Hao, Peng and Zhang, J. Theoret. Probab. 34 (2021); Zhang, Ann. Probab. 42(5) (2012); Zhang, Ann. Probab. 45 (2017)]. In this paper, we derive a simple inequality as a replacement of Norris type lemma and use it to show that two families of degenerate SDEs with stable like noises admit smooth density functions.
subject: Articles
  topic: section
subject: Malliavin calculus
  topic: keywords
subject: smooth density
  topic: keywords
subject: stochastic differential equation
  topic: keywords
subject: degenerate stable type noise
  topic: keywords
creator: Lihu Xu
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2025-11-17
publication date: 2025-11-17
starting page: 525
ending page: 549
doi: 10.4208/cmaa.2025-0015

Asymptotics in Wasserstein Distance for Empirical Measures of Markov Processes
type: item
description: In this paper we introduce some recent progresses on the convergence rate in Wasserstein distance for empirical measures of Markov processes. For diffusion processes on compact manifolds possibly with reflecting or killing boundary conditions, the sharp convergence rate as well as renormalization limits are presented in terms of the dimension of the manifold and the spectrum of the generator. For general ergodic Markov processes, explicit estimates are presented for the convergence rate by using a nice reference diffusion process, which are illustrated by some typical examples. Finally, some techniques are introduced to estimate the Wasserstein distance between empirical measures.
subject: Articles
  topic: section
subject: Empirical measure
  topic: keywords
subject: Wasserstein distance
  topic: keywords
subject: Markov process
  topic: keywords
subject: Riemannian manifold
  topic: keywords
subject: eigenvalue
  topic: keywords
creator: Feng-Yu Wang
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2025-11-17
publication date: 2025-11-17
starting page: 495
ending page: 524
doi: 10.4208/cmaa.2025-0014

Preface：Special Issue on Recent Progresses in Stochastic Differential Equations and Stochastic Partial Differential Equations
type: item
subject: Articles
  topic: section
creator: Panpan Ren
creator: Jiang-Lun Wu
rights: Copyright (c) 2025 Communications in Mathematical Analysis and Applications
date: 2026-01-29
publication date: 2026-01-29
starting page: i
ending page: ii
doi: 10.4208/cmaa.v4n4.preface

Crossing Thresholds in High Contrast Boundary Homogenization Problems: A Review
type: item
description: In this paper we provide a review of the state of the art in two topics of the homogenization theory: boundary homogenization for rapidly alternating boundary conditions on grill-type walls and homogenization of linear or nonlinear Robin boundary conditions in perforate media. High contrasts on the Robin boundary conditions are introduced. These contrasts are represented by new parameters and, along with the period and the sizes of “grill-crossing points”/perforations, play an important role in determining “thresholds” marking changes in the homogenized boundary conditions, either with “averaged terms” or “strange terms” or, somehow, “extreme” asymptotic behaviors for the solutions. Taking into account the advances of the last years in the topics, we also overview vector problems (cf. Winkler-Robin boundary conditions) and models in perforated media of interest in material sciences among others.
subject: Articles
  topic: section
subject: Boundary homogenization
  topic: keywords
subject: high contrasts
  topic: keywords
subject: nonlinear boundary conditions
  topic: keywords
subject: Robin conditions
  topic: keywords
subject: Winkler conditions
  topic: keywords
subject: strange term
  topic: keywords
subject: critical relations.
  topic: keywords
subject: 35B27
  topic: subjects
subject: 74Q20
  topic: subjects
subject: 35J65
  topic: subjects
subject: 35J88
  topic: subjects
subject: 35J05
  topic: subjects
subject: 35P05
  topic: subjects
subject: 35C20
  topic: subjects
creator: Maria-Eugenia Pérez-Martínez
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-02
publication date: 2025-09-02
starting page: 438
ending page: 494
doi: 10.4208/cmaa.2025-0013

Variational Functionals for the Characterization of BV and Sobolev Spaces
type: item
description: This paper examines the characterization of bounded variation (BV) and Sobolev functions by using some non-local functionals. We analyze their pointwise convergence and establish a connection with the Sobolev norm and the total variation measure. By investigating a wider class of non local functionals, we provide a deeper understanding of how these approximations capture the local properties of BV and Sobolev spaces, thereby reinforcing their applicability in the Euclidean setting.
subject: Articles
  topic: section
subject: BMO-type seminorms
  topic: keywords
subject: Sobolev spaces
  topic: keywords
subject: functions of bounded variation.
  topic: keywords
subject: 46E35
  topic: subjects
subject: 26A45
  topic: subjects
creator: Serena Guarino Lo Bianco
creator: Roberta Schiattarella
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-02
publication date: 2025-09-02
starting page: 419
ending page: 437
doi: 10.4208/cmaa.2025-0012

Large Time Behavior of Solutions to Burgers Equation with a Time Delay
type: item
description: In this article, we consider the large time behavior of solutions $ρ$ to the one-dimensional Cauchy problem of the generalized viscous Burgers equations with a time delay. More precisely, we derive the time decay estimate of the solution to the Cauchy problem, provided by $ρ_0(0)∈L^1$ and $ρ_0∈C([−τ,0];H^1 ).$ The result is based on the combination of the weighted $L^2$ energy estimate and the $L^1$ estimate.
subject: Articles
  topic: section
subject: Burgers equation
  topic: keywords
subject: time delay
  topic: keywords
subject: large time behavior.
  topic: keywords
subject: 35B40
  topic: subjects
subject: 35Q35
  topic: subjects
creator: Takayuki Kubo
creator: Yoshihiro Ueda
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-02
publication date: 2025-09-02
starting page: 392
ending page: 418
doi: 10.4208/cmaa.2025-0011

Multi-Level Structured Deformations: Relaxation via a Global Method Approach
type: item
description: We present some relaxation and integral representation results for energy functionals in the setting of structured deformations, with special emphasis given to the case of multi-level structured deformations. In particular, we present an integral representation result for an abstract class of variational functionals in this framework via a global method for relaxation and identify, under quite general assumptions, the corresponding relaxed energy densities through the study of a related local Dirichlet-type problem. Some applications to specific relaxation problems are also mentioned, showing that our global method approach recovers some previously established results.
subject: Articles
  topic: section
subject: Global method for relaxation
  topic: keywords
subject: hierarchical system of structured deformations
  topic: keywords
subject: multi-scale geometry
  topic: keywords
subject: disarrangements
  topic: keywords
subject: integral representation.
  topic: keywords
subject: 49J45
  topic: subjects
subject: 46E30
  topic: subjects
subject: 74A60
  topic: subjects
subject: 74M99
  topic: subjects
subject: 74B20
  topic: subjects
creator: Ana Cristina Barroso
creator: José Matias
creator: Elvira Zappale
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-02
publication date: 2025-09-02
starting page: 368
ending page: 391
doi: 10.4208/cmaa.2025-0010

Homogenization of an Elliptic System Involving Non-Local and Equi-Valued Interface Conditions
type: item
description: In this paper, we analyze the effective behaviour of the solution of an elliptic problem in a two-phase composite material with non-standard imperfect contact conditions between its constituents. More specifically, we consider on the interface an equi-valued surface condition and a non-local flux condition involving a scaling parameter $α.$ We perform a homogenization procedure by using the periodic unfolding technique. As a result, we obtain two different effective models, depending on the scaling parameter $α.$ More precisely, in the case $α > −1,$ we are led to a standard Dirichlet problem for an elliptic equation, while in the case $α = −1,$ we get a bidomain system, consisting in the coupling of an elliptic equation with an algebraic one.
subject: Articles
  topic: section
subject: Periodic homogenization
  topic: keywords
subject: non-local transmission conditions
  topic: keywords
subject: equi-valued interface conditions
  topic: keywords
subject: elliptic systems.
  topic: keywords
subject: 35B27
  topic: subjects
subject: 35J25
  topic: subjects
subject: 35Q79
  topic: subjects
creator: Micol Amar
creator: Daniele Andreucci
creator: Claudia Timofte
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-02
publication date: 2025-09-02
starting page: 347
ending page: 367
doi: 10.4208/cmaa.2025-0009

Uncertainty and Strichartz Type Inequalities for Fractional Hajłasz-Sobolev Spaces
type: item
description: In this paper we obtain uncertainty and Strichartz type inequalities for fractional Hajłasz-Sobolev spaces in the metric setting.
subject: Articles
  topic: section
subject: Metric measure space
  topic: keywords
subject: rearrangement invariant spaces
  topic: keywords
subject: uncertainty inequality
  topic: keywords
subject: Besov spaces.
  topic: keywords
subject: 46E35
  topic: subjects
subject: 46E30
  topic: subjects
subject: 30L99
  topic: subjects
creator: Joaquim Martín
creator: Walter A. Ortiz
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-02
publication date: 2025-09-02
starting page: 336
ending page: 346
doi: 10.4208/cmaa.2025-0008

On the Eigenvalue Problem for a Bulk/Surface Elliptic System
type: item
description: The paper addresses the doubly elliptic eigenvalue problem where $Ω$ is a bounded open subset of $\mathbb{R}^N$ $(N ≥ 2)$ with a $C^1$ boundary $Γ = Γ_0∪Γ_1,$ $Γ_0∩Γ_1 = ∅,$ $Γ_1$ being nonempty and relatively open on $Γ.$ Moreover, $\mathcal{H}^{N-1}(\overline{\Gamma}_0 \cap \overline{\Gamma}_1)=0$ and $\mathcal{H}^{N−1} (Γ_0) > 0.$ We prove that $L^2 (Ω)×L^2 (Γ_1)$ admits a Hilbert basis constituted by eigenfunctions and we describe the behavior of the eigenvalues. Moreover, when $Γ$ is at least $C^2$ and $\overline{Γ}_0∩\overline{Γ}_1=∅,$ we give several qualitative properties of the eigenfunctions.
subject: Articles
  topic: section
subject: Bulk/surface
  topic: keywords
subject: elliptic system
  topic: keywords
subject: eigenvalue problem
  topic: keywords
subject: oscillation modes
  topic: keywords
subject: standing solutions
  topic: keywords
subject: hyperbolic dynamic boundary conditions
  topic: keywords
subject: wave equation.
  topic: keywords
subject: 35J05
  topic: subjects
subject: 35J20
  topic: subjects
subject: 35J25
  topic: subjects
subject: 35J57
  topic: subjects
subject: 35L05
  topic: subjects
subject: 35L10
  topic: subjects
creator: Enzo Vitillaro
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-02
publication date: 2025-09-02
starting page: 307
ending page: 335
doi: 10.4208/cmaa.2025-0007

Preface: Proceedings of the International Conference on Elliptic and Parabolic Problems, Gaeta, Italy, 20-24 May 2024
type: item
subject: Articles
  topic: section
subject:
  topic: keywords
subject:
  topic: subjects
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-09-02
publication date: 2025-09-02
starting page: i
ending page: ii
doi: 10.4208/cmaa.v4n3.preface

Decay Structure of the Zener-Type Viscoelastic Plate with Type II Heat Conduction in the Whole Space
type: item
description: In this paper, we study the Zener-type viscoelastic plate in that heat conduction is determined by the type II Green-Naghdi theory. This model considers the finite propagation of thermal waves, which is compatible with the causality principle. We consider the Cauchy problem of this model and derive the decay estimates of solutions. Furthermore, the optimality of the decay estimate is discussed.
subject: Articles
  topic: section
subject: Zener-type viscoelastic plate
  topic: keywords
subject: type II Green-Naghdi theory
  topic: keywords
subject: dissipative structure.
  topic: keywords
subject: 35Q79
  topic: subjects
subject: 74H40
  topic: subjects
subject: 74K20
  topic: subjects
creator: Etsuto Adachi
creator: Ramon Quintanilla
creator: Yoshihiro Ueda
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-03
publication date: 2025-06-03
starting page: 296
ending page: 306
doi: 10.4208/cmaa.2025-0006

Suppression of Chemotactic Singularity via Poiseuille Flow in a Self-Consistent Patlak-Keller-Segel-Navier-Stokes System
type: item
description: In this paper, we investigate a fully parabolic Patlak-Keller-Segel-Navier-Stokes system with a self-consistent mechanism near the Poiseuille flow $A(y^2,0)$ in $\mathbb{T}×\mathbb{R},$ which is more natural than the Couette flow from a biomathematical perspective. We demonstrate that the solution to this system maintains global regularity, provided the amplitude $A$ is suitably large and the non-zero modes of the initial chemical density and vorticity are suitably small. To avoid the complex study of the spectral properties of the linear operator and its resolvent, we prove our result using a straightforward weighted energy method combined with a bootstrap argument.
subject: Articles
  topic: section
subject: Suppression of chemotactic singularity
  topic: keywords
subject: Poiseuille flow
  topic: keywords
subject: self-consistent
  topic: keywords
subject: fully parabolic Patlak-Keller-Segel-Navier-Stokes system.
  topic: keywords
subject: 35K55
  topic: subjects
subject: 35Q92
  topic: subjects
subject: 35Q35
  topic: subjects
subject: 92C17
  topic: subjects
creator: Hao Li
creator: Yingping Peng
creator: Zhaoyin Xiang
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-03
publication date: 2025-06-03
starting page: 234
ending page: 284
doi: 10.4208/cmaa.2025-0004

Compact Embeddings and Pitt’s Property for Weighted Sequence Spaces of Sobolev Type
type: item
description: In this article we introduce a new class of weighted sequence spaces of Sobolev type and prove several compact embedding theorems for them. It is our contention that the chosen class is general enough so as to allow applications in various areas of mathematics and mathematical physics. In particular, our results constitute a generalization of those compact embeddings recently obtained in relation to the spectral analysis of a class of master equations arising in non-equilibrium statistical mechanics. As a byproduct of our considerations, we also prove a theorem of Pitt’s type asserting that under some conditions every linear bounded operator acting between such weighted spaces is compact.
subject: Articles
  topic: section
subject: Sobolev sequence spaces
  topic: keywords
subject: Pitt’s property.
  topic: keywords
subject: Primary: 46B50;Secondary: 46E35
  topic: subjects
creator: Pierre-A. Vuillermot
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-03
publication date: 2025-06-03
starting page: 285
ending page: 295
doi: 10.4208/cmaa.2025-0005

Localization and Multiplicity for Stationary Stokes Systems with Variable Viscosity
type: item
description: In this paper we discuss the localization and the multiplicity of solutions for the stationary Stokes system with variable viscosity and a reaction force term. The results obtained apply to systems with strongly oscillating periodic viscosity and the corresponding homogenized systems.
subject: Articles
  topic: section
subject: Stokes system
  topic: keywords
subject: localization and multiplicity of solutions
  topic: keywords
subject: fixed point method
  topic: keywords
subject: homogenization.
  topic: keywords
subject: 35Q30
  topic: subjects
subject: 47J05
  topic: subjects
creator: Renata Bunoiu
creator: Radu Precup
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-03
publication date: 2025-06-03
starting page: 151
ending page: 178
doi: 10.4208/cmaa.2025-0001

A Note on the Global Existence in a Fully Parabolic Patlak-Keller-Segel-Navier-Stokes System
type: item
description: This paper is concerned with a fully parabolic Patlak-Keller-Segel-Navier-Stokes system where $Ω ⊂\mathbb{R}^2$ is a smoothly bounded domain and the parameter $χ$ is positive. The main aim of this note is to show that if then the solution of the above system is global and bounded in time.
subject: Articles
  topic: section
subject: Global existence
  topic: keywords
subject: boundedness
  topic: keywords
subject: Patlak-Keller-Segel-Navier-Stokes.
  topic: keywords
subject: 35B35
  topic: subjects
subject: 35B40
  topic: subjects
subject: 35B45
  topic: subjects
subject: 35K55
  topic: subjects
creator: Pan Zheng
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-03
publication date: 2025-06-03
starting page: 179
ending page: 201
doi: 10.4208/cmaa.2025-0002

Local Well-Posedness and Weak-Strong Uniqueness to the Incompressible Vlasov-MHD System
type: item
description: In this paper, we investigate the local well-posedness of strong solutions and weak-strong uniqueness property to the incompressible Vlasov-magnetohydrodynamic (Vlasov-MHD) model in $\mathbb{R}^3_x.$ This model consists of a Vlasov equation and the incompressible MHD equations, which interact via the so-called Lorentz force. We first establish the local well-posedness of a strong solution $(f ,u,B)$ by utilizing the delicate energy method for the iteration sequence of approximate solutions, provided that the initial data $(f_0,u_0,B_0)$ are $H^2$-regular and $f_0(x,v)$ has a compact support in the velocity $v.$ We further demonstrate the weak-strong uniqueness property of solutions if $f_0(x,v)∈L^1∩L^∞(\mathbb{R}^3_x×\mathbb{R}^3_v),$ and thereby establish a rigorous connection between the strong and weak solutions to the Vlasov-MHD system. The absence of a dissipation structure in the Vlasov equation and the presence of the strong trilinear coupling term $((u−v)×B)f$ in the model pose significant challenges in deriving our results. To address these issues, we employ the method of characteristics to estimate the size of the support of $f,$ which enables us to overcome the difficulties associated with evaluating the integral $\int_{\mathbb{R}^3} ((u−v)×B)f {\rm d}v.$
subject: Articles
  topic: section
subject: Incompressible Vlasov-MHD system
  topic: keywords
subject: local well-posedness
  topic: keywords
subject: weak-strong uniqueness property
  topic: keywords
subject: energy method.
  topic: keywords
subject: 35Q83
  topic: subjects
subject: 76W05
  topic: subjects
subject: 35B35
  topic: subjects
creator: Fucai Li
creator: Jinkai Ni
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-06-03
publication date: 2025-06-03
starting page: 202
ending page: 233
doi: 10.4208/cmaa.2025-0003

A Constructive Proof of Korn’s Scaled Inequalities for Shells
type: item
description: One of Korn’s scaled inequalities for shells asserts that the $H^1$-norm of a displacement field of a shell with thickness $2ε$ clamped on a portion of its lateral boundary, once scaled to a domain independent of $ε,$ is bounded above by the $L^2$-norm of the corresponding scaled infinitesimal strain tensor field multiplied by a constant of order $ε^{−1}.$ We give a constructive proof to this inequality, and to other two inequalities of this type, which is thus different from the original proof of Ciarlet et al. [Arch. Rational Mech. Anal. 136 (1996), 163–190].
subject: Articles
  topic: section
subject: Korn inequalities
  topic: keywords
subject: shells
  topic: keywords
subject: asymptotic analysis.
  topic: keywords
subject: 74K25
  topic: subjects
subject: 74G45
  topic: subjects
subject: 35B40
  topic: subjects
creator: Cristinel Mardare
creator: Thai Ha Nguyen
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-02-10
publication date: 2025-02-10
starting page: 87
ending page: 111
doi: 10.4208/cmaa.2024-0007

The Biot Stress-Right Stretch Relation for the Compressible Neo-Hooke-Ciarlet-Geymonat Model and Rivlin’s Cube Problem
type: item
description: The aim of the paper is to recall the importance of the study of invertibility and monotonicity of stress-strain relations for investigating the nonuniqueness and bifurcation of homogeneous solutions of the equilibrium problem of a hyperelastic cube subjected to equiaxial tensile forces. In other words, we reconsider a remarkable possibility in this nonlinear scenario: Does symmetric loading lead only to symmetric deformations or also to asymmetric deformations? If so, what can we say about monotonicity for these homogeneous solutions, a property which is less restrictive than the energetic stability criteria of homogeneous solutions for Rivlin’s cube problem. For the Neo-Hooke type materials we establish what properties the volumetric function $h$ depending on ${\rm det}F$ must have to ensure the existence of a unique radial solution (i.e. the cube must continue to remain a cube) for any magnitude of radial stress acting on the cube. The function $h$ proposed by Ciarlet and Geymonat satisfies these conditions. However, discontinuous equilibrium trajectories may occur, characterized by abruptly appearing non-symmetric deformations with increasing load, and a cube can instantaneously become a parallelepiped. Up to the load value for which the bifurcation in the radial solution is realized local monotonicity holds true. However, after exceeding this value, monotonicity no longer occurs on homogeneous deformations which, in turn, preserve the cube shape.
subject: Articles
  topic: section
subject: Neo-Hooke-Ciarlet-Geymonat
  topic: keywords
subject: bifurcation
  topic: keywords
subject: Rivlin’s cube problem
  topic: keywords
subject: invertibility
  topic: keywords
subject: Hilbert-monotonicity
  topic: keywords
subject: Biot stress-stretch relation.
  topic: keywords
subject: 73G05
  topic: subjects
subject: 73G10
  topic: subjects
subject: 73H05
  topic: subjects
creator: Ionel-Dumitrel Ghiba
creator: Franz Gmeineder
creator: Sebastian Holthausen
creator: Robert J. Martin
creator: Patrizio Neff
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-02-10
publication date: 2025-02-10
starting page: 112
ending page: 150
doi: 10.4208/cmaa.2024-0026

Preface: Asymptotic Analysis and Elasticity Theory: A Collection of Papers Dedicated to Professor Philippe G. Ciarlet on the Occasion of His 85th Birthday
type: item
subject: Articles
  topic: section
subject:
  topic: subjects
rights: Copyright (c) 2025 COPYRIGHT: © Global Science Press
date: 2025-02-10
publication date: 2025-02-10
starting page: i
ending page: iii
doi: 10.4208/cmaa.v4n1.preface