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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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

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

First available in Project Euclid: 25 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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