Existence and blow up in a system of wave equations with nonstandard nonlinearities

Electronic Journal of Differential Equations

article

Salim A. Messaoudi¹  Oulia Bouhoufani²  Ilhem Hamchi²  Mohamed Alahyane³ 

[1] Department of Mathematics University of Sharjah P. O. Box 27272 Sharjah United Arab Emirates;Department of Mathematics University Batna-2 05000 Batna;Department of Mathematics, RISE University of Sharjah P. O. Box 27272 Sharjah United Arab Emirates

关键词: Hyperbolic system;    existence;    blow up;    variable exponents;    nonlinear.;   

DOI  :  10.58997/ejde.2021.91

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

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 oint 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.

【 授权许可】

CC BY