Blow-Up of Solutions to Boundary Value Problems of Coupled Wave Equations with Damping Terms on Exterior Domain (Journal of Mathematical Study, 2024)
This paper is concerned with blow-up dynamics of solutions to coupled systems of damped inhomogeneous wave equations with power nonlinearities related toweight function $t^α|x|^β$ and variable boundary conditions on an exterior domain. Thedamping terms investigated in this work contain weak damping terms and convectionterms. In terms of the Neumann-type boundary conditions and Dirichlet-type boundary conditions, the non-existence of global solutions to the problems is demonstratedby constructing appropriate test functions and applying contradiction arguments, respectively. Our main new contributions are that the effects of damping terms and nonlinear terms on behaviors of solutions to the coupled inhomogeneous wave equationsare 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.