Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms

Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms

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 g...

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Main Authors: Zhigang Pan, Hong Luo, Tian Ma
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/805158
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spelling doaj-30c83013e32e47d48129995be46dfbbd2020-11-25T00:17:14ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/805158805158Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped TermsZhigang Pan0Hong Luo1Tian Ma2Yangtze Center of Mathematics, Sichuan University, Chengdu, Sichuan 610041, ChinaCollege of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, ChinaYangtze Center of Mathematics, Sichuan University, Chengdu, Sichuan 610041, ChinaWe 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 u∈Lloc∞((0,∞),W2,p(Ω)∩W01,p(Ω)).http://dx.doi.org/10.1155/2012/805158
collection DOAJ
language English
format Article
sources DOAJ
author Zhigang Pan
Hong Luo
Tian Ma
spellingShingle Zhigang Pan
Hong Luo
Tian Ma
Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms
Journal of Applied Mathematics
author_facet Zhigang Pan
Hong Luo
Tian Ma
author_sort Zhigang Pan
title Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms
title_short Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms
title_full Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms
title_fullStr Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms
title_full_unstemmed Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms
title_sort global existence of strong solutions to a class of fully nonlinear wave equations with strongly damped terms
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description 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 u∈Lloc∞((0,∞),W2,p(Ω)∩W01,p(Ω)).
url http://dx.doi.org/10.1155/2012/805158
work_keys_str_mv AT zhigangpan globalexistenceofstrongsolutionstoaclassoffullynonlinearwaveequationswithstronglydampedterms
AT hongluo globalexistenceofstrongsolutionstoaclassoffullynonlinearwaveequationswithstronglydampedterms
AT tianma globalexistenceofstrongsolutionstoaclassoffullynonlinearwaveequationswithstronglydampedterms
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