New Class of Kirchhoff Type Equations with Kelvin-Voigt Damping and General Nonlinearity: Local Existence and Blow-up in Solutions
Year: 2021
Author: Hanni Dridi, Khaled Zennir
Journal of Partial Differential Equations, Vol. 34 (2021), Iss. 4 : pp. 313–347
Abstract
In this paper, we consider a class of Kirchhoff equation, in the presence of a Kelvin-Voigt type damping and a source term of general nonlinearity forms. Where the studied equation is given as follows
utt−K(Nu(t))[Δp(x)u+Δr(x)ut]=F(x,t,u).
Here, K(Nu(t)) is a Kirchhoff function, Δr(x)ut represent a Kelvin-Voigt strong damping term, and F(x,t,u) is a source term. According to an appropriate assumption, we obtain the local existence of the weak solutions by applying the Galerkin's approximation method. Furthermore, we prove a non-global existence result for certain solutions with negative/positive initial energy. More precisely, our aim is to find a sufficient conditions for p(x),q(x),r(x),F(x,t,u) and the initial data for which the blow-up occurs.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v34.n4.2
Journal of Partial Differential Equations, Vol. 34 (2021), Iss. 4 : pp. 313–347
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Galerkin approximation variable exponents Kirchhoff equation blow-up of solutions Kelvin-Voigt damping general nonlinearity.
Author Details
Hanni Dridi Email
Khaled Zennir Email
-
Propagation of Surface Waves in a Rotating Coated Viscoelastic Half-Space under the Influence of Magnetic Field and Gravitational Forces
Mubaraki, Ali | Althobaiti, Saad | Nuruddeen, Rahmatullah IbrahimFractal and Fractional, Vol. 5 (2021), Iss. 4 P.250
https://doi.org/10.3390/fractalfract5040250 [Citations: 6] -
Operator Theory - Recent Advances, New Perspectives and Applications
Stabilization of a Quantum Equation under Boundary Connections with an Elastic Wave Equation
Dridi, Hanni
2023
https://doi.org/10.5772/intechopen.106324 [Citations: 0]