Wave equations and reaction-diffusion equations with several nonlinear source terms with critical energy

Abstract

We study the initial boundary value problem of wave equations and reaction-diffusion equations with several nonlinear source terms of different sign. For the problem with critical initial data E(0) = d(orJ(u0) = d), I(u0)<0, we prove the global nonexistence of solution under some conditions, which solves the open problem existing in [Liu Yacheng, Xu Runzhang. Wave equations and reaction-diffusion equations with several nonlinear source terms of different sign, Discrete and Continuous Dynamical System-Series B, 2007, 7(1):171-189.]