TY - JOUR
T1 - Blow-Up of Solutions to Boundary Value Problems of Coupled Wave Equations with Damping Terms on Exterior Domain
AU - Ming , Sen
AU - Du , Jiayi
AU - Xie , Jin
AU - Wu , Xiao
JO - Journal of Mathematical Study
VL - 2
SP - 194
EP - 222
PY - 2024
DA - 2024/06
SN - 57
DO - http://doi.org/10.4208/jms.v57n2.24.05
UR - https://global-sci.org/intro/article_detail/jms/23169.html
KW - Coupled system, inhomogeneous wave equations, exterior domain, test function technique, blow-up.
AB - <p style="text-align: justify;">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.</p>