Well-Posedness and Convergence Analysis of a Nonlocal Model with Singular Matrix Kernel

Well-Posedness and Convergence Analysis of a Nonlocal Model with Singular Matrix Kernel

Year:    2023

Author:    Mengna Yang, Yufeng Nie

International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 478–496

Abstract

In this paper, we consider a two-dimensional linear nonlocal model involving a singular matrix kernel. For the initial value problem, we first give well-posedness results and energy conservation via Fourier transform. Meanwhile, we also discuss the corresponding Dirichlet-type nonlocal boundary value problems in the cases of both positive and semi-positive definite kernels, where the core is the coercivity of bilinear forms. In addition, in the limit of vanishing nonlocality, the solution of the nonlocal model is seen to converge to a solution of its classical elasticity local model provided that $c_t = 0.$

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ijnam2023-1020

International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 478–496

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Nonlocal model well-posedness convergence singular matrix kernel coercivity.

Author Details

Mengna Yang

Yufeng Nie