Volume 57, Issue 2
Blow-Up of Solutions to Boundary Value Problems of Coupled Wave Equations with Damping Terms on Exterior Domain

Sen Ming, Jiayi Du, Jin Xie & Xiao Wu

J. Math. Study, 57 (2024), pp. 194-222.

Published online: 2024-06

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  • 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.

  • AMS Subject Headings

35L70, 58J45

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COPYRIGHT: © Global Science Press

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@Article{JMS-57-194, author = {Ming , SenDu , JiayiXie , Jin and Wu , Xiao}, title = {Blow-Up of Solutions to Boundary Value Problems of Coupled Wave Equations with Damping Terms on Exterior Domain}, journal = {Journal of Mathematical Study}, year = {2024}, volume = {57}, number = {2}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v57n2.24.05}, url = {http://global-sci.org/intro/article_detail/jms/23169.html} }
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 -

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.

Ming , SenDu , JiayiXie , Jin and Wu , Xiao. (2024). Blow-Up of Solutions to Boundary Value Problems of Coupled Wave Equations with Damping Terms on Exterior Domain. Journal of Mathematical Study. 57 (2). 194-222. doi:10.4208/jms.v57n2.24.05
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