Interplay effects on blow-up of weakly coupled systems for semilinear wave equations with general nonlinear memory terms

Abstract

In this paper, we study weakly coupled systems for semilinear wave equations with distinct nonlinear memory terms in general forms, and the corresponding single semilinear equation with general nonlinear memory terms. Thanks to Banach's fixed point theorem, we prove local (in time) existence of solutions with the $L^1$ assumption on the memory kernels. Then, blow-up results for energy solutions are derived applying iteration methods associated with slicing procedure. We investigate interactions on the blow-up conditions under different decreasing assumptions on the memory term. Particularly, a new threshold for the kernels on interplay effect is found. Additionally, we give some applications of our results on semilinear wave equations and acoustic wave equations.

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• A note on blow-up results for semilinear wave equations in de Sitter and anti-de Sitter spacetimes
• A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term
• A blow-up result for a Nakao-type weakly coupled system with nonlinearities of derivative-type
• Estimates for the nonlinear viscoelastic damped wave equation on compact Lie groups