Blow-Up of Solutions to Boundary Value Problems of Coupled Wave Equations with Damping Terms on Exterior Domain

Abstract

This paper is concerned with blow-up dynamics of solutions to coupled sys- tems of damped inhomogeneous wave equations with power nonlinearities related to weight function t^α|x|^β and variable boundary conditions on an exterior domain. The damping terms investigated in this work contain weak damping terms and convection terms. In terms of the Neumann-type boundary conditions and Dirichlet-type bound- ary conditions, the non-existence of global solutions to the problems is demonstrated by constructing appropriate test functions and applying contradiction arguments, re- spectively. Our main new contributions are that the effects of damping terms and non- linear terms on behaviors of solutions to the coupled inhomogeneous wave equations are analyzed. As far as the authors know, the results in Theorems 1.1-1.4 are new

Keywords

Coupled system / inhomogeneous wave equations / exterior domain / test function technique / blow-up