Advances in Differential Equations

On the Korteweg-de Vries-Kuramoto-Sivashinsky equation

H. A. Biagioni, J. L. Bona, R. J. Iório, and M. Scialom

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Abstract

Considered herein is the Korteweg-de Vries equation with a Kuramoto-Sivashinsky dissipative term appended. This evolution equation, which arises as a model for a number of interesting physical phenomena, has been extensively investigated in a recent paper of Ercolani, McLaughlin and Roitner. The numerical simulations of the initial-value problem reported in the just-mentioned study showed solutions to possess a more complex range of behavior than the unadorned Korteweg-de Vries equation. The present work contributes some basic analytical facts relevant to the initial-value problem and to some of the conclusions drawn by Ercolanet al. In addition to showing the initial-value problem is well posed, we determine the limiting behavior of solutions as the dissipative or the dispersive parameter tends to zero.

Article information

Source
Adv. Differential Equations Volume 1, Number 1 (1996), 1-20.

Dates
First available in Project Euclid: 25 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366896312

Mathematical Reviews number (MathSciNet)
MR1357952

Zentralblatt MATH identifier
0844.35103

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Citation

Biagioni, H. A.; Bona, J. L.; Iório, R. J.; Scialom, M. On the Korteweg-de Vries-Kuramoto-Sivashinsky equation. Adv. Differential Equations 1 (1996), no. 1, 1--20. https://projecteuclid.org/euclid.ade/1366896312.


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