Blow-Up of Solutions to Boundary Value Problems of Coupled Wave Equations with Damping Terms on Exterior Domain
Year: 2024
Author: Sen Ming, Jiayi Du, Jin Xie, Xiao Wu
Journal of Mathematical Study, Vol. 57 (2024), Iss. 2 : pp. 194–222
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v57n2.24.05
Journal of Mathematical Study, Vol. 57 (2024), Iss. 2 : pp. 194–222
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
Keywords: Coupled system inhomogeneous wave equations exterior domain test function technique blow-up.