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1996 On the Korteweg-de Vries-Kuramoto-Sivashinsky equation
H. A. Biagioni, J. L. Bona, R. J. Iório Jr., M. Scialom
Adv. Differential Equations 1(1): 1-20 (1996). DOI: 10.57262/ade/1366896312


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.


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H. A. Biagioni. J. L. Bona. R. J. Iório Jr.. M. Scialom. "On the Korteweg-de Vries-Kuramoto-Sivashinsky equation." Adv. Differential Equations 1 (1) 1 - 20, 1996.


Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0844.35103
MathSciNet: MR1357952
Digital Object Identifier: 10.57262/ade/1366896312

Primary: 35Q53

Rights: Copyright © 1996 Khayyam Publishing, Inc.


Vol.1 • No. 1 • 1996
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