Existence and blow up in a system of wave equations with nonstandard nonlinearities
Date
2021-11-16
Authors
Messaoudi, Salim A.
Bouhoufani, Oulia
Ilhem, Hamchi
Alahyane, Mohamed
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we consider a coupled system of two nonlinear hyperbolic equations, where the exponents in the damping and source terms are variables. First, we prove a theorem of existence and uniqueness of weak solution, by using the Faedo Galerkin approximations and the Banach fixed point theorem. Then, using the energy method, we show that certain solutions with positive initial energy blow up in finite time. We also give some numerical applications to illustrate our theoretical results.
Description
Keywords
Hyperbolic system, Existence, Blow up, Variable exponents, Nonlinear
Citation
Messaoudi, S. A., Bouhoufani, O., Hamchi, I., & Alahyane, M. (2021). Existence and blow up in a system of wave equations with nonstandard nonlinearities. <i>Electronic Journal of Differential Equations, 2021</i>(91), pp. 1-33.
Rights
Attribution 4.0 International