Curtin University Homepage
  • Library
  • Help
    • Admin

    espace - Curtin’s institutional repository

    JavaScript is disabled for your browser. Some features of this site may not work without it.
    View Item 
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item

    Global solutions and blow-up phenomena to a shallow water equation

    Access Status
    Open access via publisher
    Authors
    Lai, S.
    Wu, Yonghong
    Date
    2010
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Lai, Shaoyong and Wu, Yonghong. 2010. Global solutions and blow-up phenomena to a shallow water equation. Journal of Differential Equations. 249 (3): pp. 693-706.
    Source Title
    Journal of Differential Equations
    DOI
    10.1016/j.jde.2010.03.008
    ISSN
    00220396
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/37786
    Collection
    • Curtin Research Publications
    Abstract

    A nonlinear shallow water equation, which includes the famous Camassa–Holm (CH) and Degasperis–Procesi (DP) equations as special cases, is investigated. The local well-posedness of solutions for the nonlinear equation in the Sobolev space Hs(R) with is developed. Provided that does not change sign, u0∈Hs () and u0∈L1(R), the existence and uniqueness of the global solutions to the equation are shown to be true in u(t,x)∈C([0,∞);Hs(R))∩C1([0,∞);Hs−1(R)). Conditions that lead to the development of singularities in finite time for the solutions are also acquired.

    Related items

    Showing items related by title, author, creator and subject.

    • The well-posedness and solutions of Boussinesq-type equations
      Lin, Qun (2009)
      We develop well-posedness theory and analytical and numerical solution techniques for Boussinesq-type equations. Firstly, we consider the Cauchy problem for a generalized Boussinesq equation. We show that under suitable ...
    • Numerical Solution of Second-Order Linear Fredholm Integro-Differential Equation Using Generalized Minimal Residual Method
      Aruchunan, Elayaraja; Sulaiman, J. (2010)
      This research purposely brought up to solve complicated equations such as partial differential equations, integral equations, Integro-Differential Equations (IDE), stochastic equations and others. Many physical phenomena ...
    • All traveling wave exact solutions of three kinds of nonlinear evolution equations
      Meng, F.; Zhang, L.; Wu, Yong Hong; Yuan, W. (2015)
      In this article, we employ the complex method to obtain all meromorphic exact solutions of complex Klein–Gordon (KG) equation, modified Korteweg-de Vries (mKdV) equation, and the generalized Boussinesq (gB) equation at ...
    Advanced search

    Browse

    Communities & CollectionsIssue DateAuthorTitleSubjectDocument TypeThis CollectionIssue DateAuthorTitleSubjectDocument Type

    My Account

    Admin

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Follow Curtin

    • 
    • 
    • 
    • 
    • 

    CRICOS Provider Code: 00301JABN: 99 143 842 569TEQSA: PRV12158

    Copyright | Disclaimer | Privacy statement | Accessibility

    Curtin would like to pay respect to the Aboriginal and Torres Strait Islander members of our community by acknowledging the traditional owners of the land on which the Perth campus is located, the Whadjuk people of the Nyungar Nation; and on our Kalgoorlie campus, the Wongutha people of the North-Eastern Goldfields.