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

[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.

[学科分类] 数学（综合）

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