On a nonlocal analog of the kuramoto-sivashinsky equation
We study a nonlocal equation, analogous to the Kuramoto-Sivashinsky equation, in which short waves are stabilized by a possibly fractional diffusion of order less than or equal to two, and long waves are destabilized by a backward fractional diffusion of lower order. We prove the global existence, u...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Universidad de Cantabria (UC) |
| Repository: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Language: | French |
| OAI Identifier: | oai:repositorio.unican.es:10902/29547 |
| Online Access: | https://hdl.handle.net/10902/29547 |
| Access Level: | Open access |
| Keyword: | Kuramoto-Sivashinsky equation Spatial chaos Attractor |
| Summary: | We study a nonlocal equation, analogous to the Kuramoto-Sivashinsky equation, in which short waves are stabilized by a possibly fractional diffusion of order less than or equal to two, and long waves are destabilized by a backward fractional diffusion of lower order. We prove the global existence, uniqueness, and analyticity of solutions of the nonlocal equation and the existence of a compact attractor. Numerical results show that the equation has chaotic solutions whose spatial structure consists of interacting travelling waves resembling viscous shock profiles. |
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