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On Local Existence and Blow-Up of Solutions for Nonlinear Wave Equations of Higher-Order Kirchhoff Type with Strong Dissipation
Department of Mathematics, Yunnan University, Kunming, China
Department of Mathematics, Yunnan University, Kunming, China
Department of Mathematics, Yunnan University, Kunming, China
- 1 Department of Mathematics, Yunnan University, Kunming, China
- 2 Department of Mathematics, Yunnan University, Kunming, China
- 3 Department of Mathematics, Yunnan University, Kunming, China
International Journal of Modern Nonlinear Theory and Application·Volume 06 (2017)·Pages 11–25·Published 11 January 2017·DOI10.4236/ijmnta.2017.61002
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Abstract
In this paper, we study on the initial-boundary value problem for nonlinear wave equations of higher-order Kirchhoff type with Strong Dissipation: . At first, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. Then, by “Concavity” method we establish three blow-up results for certain solutions in the case 1): , in the case 2): and in the case 3): . At last, we consider that the estimation of the upper bounds of the blow-up time is given for deferent initial energy.
KeywordsNonlinear Higher-Order Kirchhoff Type EquationStrong DampingLocal SolutionsBlow-UpInitial Energy
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