Global Well-posedness and Asymptotic Behavior of a Class of Initial-boundary-value Problems of the KdV Equation on a Finite Domain

Author(s)

Ivonne Rivas, University of Cincinnati - Main Campus
Muhammad Usman, University of DaytonFollow
Bingyu Zhang, University of Cincinnati - Main CampusFollow

Document Type

Article

Publication Date

3-2011

Publication Source

Mathematical Control and Related Fields

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.

Copyright

Copyright © 2011, American Institute of Mathematical Sciences.

Publisher

American Institute of Mathematical Sciences

Volume

1

Issue

1

Peer Reviewed

yes

Keywords

Global well-posedness, Korteweg-de Vries equation, asymptotic behavior

eCommons Citation

Rivas, Ivonne; Usman, Muhammad; and Zhang, Bingyu, "Global Well-posedness and Asymptotic Behavior of a Class of Initial-boundary-value Problems of the KdV Equation on a Finite Domain" (2011). Mathematics Faculty Publications. 9.
https://ecommons.udayton.edu/mth_fac_pub/9