Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $|x|oinfty$

We prove a comparison principle for solutions of the Cauchy problem of the nonlinear pseudoparabolic equation $u_t=Delta u_t+ Deltavarphi(u) +h(t,u)$ with nonnegative bounded initial data. We show stabilization of a maximal solution to a maximal solution of the Cauchy problem for the correspondi...

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Main Author:	Tatiana Kavitova
Format:	Article
Language:	English
Published:	Texas State University 2012-08-01
Series:	Electronic Journal of Differential Equations
Subjects:	Pseudoparabolic equation comparison principle stabilization
Online Access:	http://ejde.math.txstate.edu/Volumes/2012/141/abstr.html

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spelling	doaj-382a1ee12b2f4135a87b6c509ef1bdb42020-11-24T20:49:01ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-08-012012141,112Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $\|x\|oinfty$Tatiana KavitovaWe prove a comparison principle for solutions of the Cauchy problem of the nonlinear pseudoparabolic equation $u_t=Delta u_t+ Deltavarphi(u) +h(t,u)$ with nonnegative bounded initial data. We show stabilization of a maximal solution to a maximal solution of the Cauchy problem for the corresponding ordinary differential equation $vartheta'(t)=h(t,vartheta)$ as $\|x\|oinfty$ under certain conditions on an initial datum. http://ejde.math.txstate.edu/Volumes/2012/141/abstr.htmlPseudoparabolic equationcomparison principlestabilization
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Tatiana Kavitova
spellingShingle	Tatiana Kavitova Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $\|x\|oinfty$ Electronic Journal of Differential Equations Pseudoparabolic equation comparison principle stabilization
author_facet	Tatiana Kavitova
author_sort	Tatiana Kavitova
title	Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $\|x\|oinfty$
title_short	Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $\|x\|oinfty$
title_full	Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $\|x\|oinfty$
title_fullStr	Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $\|x\|oinfty$
title_full_unstemmed	Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $\|x\|oinfty$
title_sort	behavior of the maximal solution of the cauchy problem for some nonlinear pseudoparabolic equation as $\|x\|oinfty$
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2012-08-01
description	We prove a comparison principle for solutions of the Cauchy problem of the nonlinear pseudoparabolic equation $u_t=Delta u_t+ Deltavarphi(u) +h(t,u)$ with nonnegative bounded initial data. We show stabilization of a maximal solution to a maximal solution of the Cauchy problem for the corresponding ordinary differential equation $vartheta'(t)=h(t,vartheta)$ as $\|x\|oinfty$ under certain conditions on an initial datum.
topic	Pseudoparabolic equation comparison principle stabilization
url	http://ejde.math.txstate.edu/Volumes/2012/141/abstr.html
work_keys_str_mv	AT tatianakavitova behaviorofthemaximalsolutionofthecauchyproblemforsomenonlinearpseudoparabolicequationasxoinfty
_version_	1716807068088795136

Behavior of the maximal solution of the Cauchy problem for some nonlinear pseudoparabolic equation as $|x|oinfty$

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