Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation

We consider the Cauchy problem for the n-dimensional generalized damped Boussinesq equation. Based on decay estimates of solutions to the corresponding linear equation, we define a solution space with time weighted norms. Under small condition on the initial value, the existence and asymptotic b...

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Main Author:	Yinxia Wang
Format:	Article
Language:	English
Published:	Texas State University 2012-06-01
Series:	Electronic Journal of Differential Equations
Subjects:	Generalized damped equation global solution asymptotic behavior
Online Access:	http://ejde.math.txstate.edu/Volumes/2012/96/abstr.html

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spelling	doaj-bbbeaca3ab3843578661c27f052fafbf2020-11-25T02:47:14ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-06-01201296,111Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equationYinxia WangWe consider the Cauchy problem for the n-dimensional generalized damped Boussinesq equation. Based on decay estimates of solutions to the corresponding linear equation, we define a solution space with time weighted norms. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in the corresponding Sobolev spaces are established by the contraction mapping principle. http://ejde.math.txstate.edu/Volumes/2012/96/abstr.htmlGeneralized damped equationglobal solutionasymptotic behavior
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yinxia Wang
spellingShingle	Yinxia Wang Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation Electronic Journal of Differential Equations Generalized damped equation global solution asymptotic behavior
author_facet	Yinxia Wang
author_sort	Yinxia Wang
title	Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation
title_short	Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation
title_full	Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation
title_fullStr	Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation
title_full_unstemmed	Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation
title_sort	existence and asymptotic behavior of solutions to the generalized damped boussinesq equation
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2012-06-01
description	We consider the Cauchy problem for the n-dimensional generalized damped Boussinesq equation. Based on decay estimates of solutions to the corresponding linear equation, we define a solution space with time weighted norms. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in the corresponding Sobolev spaces are established by the contraction mapping principle.
topic	Generalized damped equation global solution asymptotic behavior
url	http://ejde.math.txstate.edu/Volumes/2012/96/abstr.html
work_keys_str_mv	AT yinxiawang existenceandasymptoticbehaviorofsolutionstothegeneralizeddampedboussinesqequation
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Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation

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