In this paper, we consider a coupled system of two nonlinear hyperbolic equations with variable-exponents in the damping and source terms. Under suitable assumptions on the intial data and the variable exponents, we prove a global existence theorem, using the Stable-set method. Then, we establish a decay estimate of the solution energy, by Komornik’s integral approach.

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.

In this paper, we consider a coupled system of two nonlinearhyperbolic equations with variable-exponents in the damping and sourceterms. Under suitable assumptions on the intial data and the variableexponents, we prove a global existence theorem, using the Stable-setmethod. Then, we establish a decay estimate of the solution energy, byKomornik’s integral approach.