Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation

Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation

We study the Cauchy problem of a weakly dissipative modified two-component Camassa-Holm equation. We firstly establish the local well-posedness result. Then we present a precise blow-up scenario. Moreover, we obtain several blow-up results and the blow-up rate of strong solutions. Finally, we consid...

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Bibliographic Details
Main Authors: Yongsheng Mi, Chunlai Mu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/547261
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spelling doaj-dbebc4202820492196ac3c00ede5abc82020-11-25T00:14:01ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/547261547261Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm EquationYongsheng Mi0Chunlai Mu1College of Mathematics and Computer Sciences, Yangtze Normal University, Chongqing, Fuling 408100, ChinaCollege of Mathematics and Statistics, Chongqing University, Chongqing 400044, ChinaWe study the Cauchy problem of a weakly dissipative modified two-component Camassa-Holm equation. We firstly establish the local well-posedness result. Then we present a precise blow-up scenario. Moreover, we obtain several blow-up results and the blow-up rate of strong solutions. Finally, we consider the asymptotic behavior of solutions.http://dx.doi.org/10.1155/2013/547261
collection DOAJ
language English
format Article
sources DOAJ
author Yongsheng Mi
Chunlai Mu
spellingShingle Yongsheng Mi
Chunlai Mu
Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation
Journal of Applied Mathematics
author_facet Yongsheng Mi
Chunlai Mu
author_sort Yongsheng Mi
title Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation
title_short Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation
title_full Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation
title_fullStr Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation
title_full_unstemmed Well-Posedness, Blow-Up Phenomena, and Asymptotic Profile for a Weakly Dissipative Modified Two-Component Camassa-Holm Equation
title_sort well-posedness, blow-up phenomena, and asymptotic profile for a weakly dissipative modified two-component camassa-holm equation
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description We study the Cauchy problem of a weakly dissipative modified two-component Camassa-Holm equation. We firstly establish the local well-posedness result. Then we present a precise blow-up scenario. Moreover, we obtain several blow-up results and the blow-up rate of strong solutions. Finally, we consider the asymptotic behavior of solutions.
url http://dx.doi.org/10.1155/2013/547261
work_keys_str_mv AT yongshengmi wellposednessblowupphenomenaandasymptoticprofileforaweaklydissipativemodifiedtwocomponentcamassaholmequation
AT chunlaimu wellposednessblowupphenomenaandasymptoticprofileforaweaklydissipativemodifiedtwocomponentcamassaholmequation
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