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Title: Blow-up of solutions for some non-linear wave equations of Kirchhoff type with some dissipation
Authors: Wu, Shun-Tang
Tsai, Long Yi
Contributors: 應數系
Keywords: Boundary value problems;Estimation;Nonlinear equations;Problem solving;Blow-up;Dissipation;Life span;Non-linear wave equations;Wave equations
Date: 2006-07
Issue Date: 2015-07-21 15:29:52 (UTC+8)
Abstract: The initial boundary value problem for non-linear wave equations of Kirchhoff type with dissipation in a bounded domain is considered. We prove the blow-up of solutions for the strong dissipative term - Δ ut and the linear dissipative term ut by the energy method and give some estimates for the life span of solutions. We also show the nonexistence of global solutions with positive initial energy for non-linear dissipative term by Vitillaro's argument. © 2005 Elsevier Ltd. All rights reserved.
Relation: Nonlinear Analysis, Theory, Methods and Applications, 65(2), 243-264
Data Type: article
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