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2012 Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equationswith Strongly Damped Terms
Zhigang Pan, Hong Luo, Tian Ma
J. Appl. Math. 2012(none): 1-15 (2012). DOI: 10.1155/2012/805158

Abstract

We consider the global existence of strong solution u, corresponding to a class of fully nonlinear wave equations with strongly damped terms utt-kΔut=f(x,Δu)+g(x,u,Du,D2u) in a bounded and smooth domain Ω in Rn, where f(x,Δu) is a given monotone in Δu nonlinearity satisfying some dissipativity and growth restrictions and g(x,u,Du,D2u) is in a sense subordinated to f(x,Δu). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solution uLloc((0,),W2,p(Ω)W01,p(Ω)).

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Zhigang Pan. Hong Luo. Tian Ma. "Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equationswith Strongly Damped Terms." J. Appl. Math. 2012 1 - 15, 2012. https://doi.org/10.1155/2012/805158

Information

Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1254.35050
MathSciNet: MR2948142
Digital Object Identifier: 10.1155/2012/805158

Rights: Copyright © 2012 Hindawi

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