Remarks on the Kuramoto-Sivashinsky equation
We report here a joint work in progress on the Kuramoto-Sivashinsky equation. The question we address is the analytical study of a fourth order nonlinear evolution equation. This equation has been obtained by Sivashinsky in the context of combustion and independently by Kuramoto in the context of reaction diffusion-systems. Both were motivated by (nonlinear) stability of travelling waves. Numerical calculations have been done on this equation. All the results seem to indicate a chaotic behavior of the solution. Therefore, the analytical study is of interest in analogy with the Burger's and Navier-Stokes equations. Here we give some existence and uniqueness results for the equation in space dimension one, and we also study a fractional step method of numerical resolution. In a forthcoming joint paper with R. Temam, we will study the asymptotic behavior, as t approaches infinity, of the solution of (0.1) and give an estimate on the number of determining modes.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 5733762
- Report Number(s):
- LA-UR-83-2862; CONF-8305110-3; ON: DE84001018
- Resource Relation:
- Conference: Fronts, interfaces and patterns conference, Los Alamos, NM, USA, 2 May 1983
- Country of Publication:
- United States
- Language:
- English
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