ON A SYSTEM OF NONLINEAR WAVE EQUATIONS

Abstract

We consider the existence and nonexistence of global solutions of the following initial-boundary value problem for a system of nonlinear wave equations in a domain Ω × [0, T): ½ utt − Δu +m21 u = −4λ(u + αv)3 − 2βuv2, vtt − Δv +m22 v = −4αλ(u + αv)3 − 2βu2v, where Ω is a bounded domain in R3 with a smooth boundary. Some sufficient conditions on the given parameters λ, α and β for the global existence and blow-up are imposed. The estimates for the lifespan of solutions is given.