(untitled) (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 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 boundary conditions, the non-existence of global solutions to the problems is demonstrated by 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 equations are analyzed. As far as the authors know, the results in Theorems 1.1-1.4 are new.