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Article
Global Well-posedness and Asymptotic Behavior of a Class of Initial-boundary-value Problems of the KdV Equation on a Finite Domain
Mathematical Control and Related Fields
  • Ivonne Rivas, University of Cincinnati - Main Campus
  • Muhammad Usman, University of Dayton
  • Bingyu Zhang, University of Cincinnati - Main Campus
Document Type
Article
Publication Date
3-1-2011
Abstract

In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg- de Vries equation posed on a ?nite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global L2 a priori estimate is not available and therefore it is not clear whether its solutions exist globally or blow up in finite time. It is shown in this paper that the solutions exist globally as long as their initial value and the associated boundary data are small, and moreover, those solutions decay exponentially if their boundary data decay exponentially.

Inclusive pages
61-81
ISBN/ISSN
2156-8472
Document Version
Postprint
Comments

The item available for download is the pre-copy-editing, author-produced PDF of an article accepted for publication in Mathematical Control and Related Fields, following peer review. The definitive publisher-authenticated version is available online.

Permission documentation is on file.

Publisher
American Institute of Mathematical Sciences
Peer Reviewed
Yes
Keywords
  • Global well-posedness,
  • Korteweg-de Vries equation,
  • asymptotic behavior
Citation Information
Ivonne Rivas, Muhammad Usman and Bingyu Zhang. "Global Well-posedness and Asymptotic Behavior of a Class of Initial-boundary-value Problems of the KdV Equation on a Finite Domain" Mathematical Control and Related Fields Vol. 1 Iss. 1 (2011)
Available at: http://works.bepress.com/muhammad_usman/10/