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...

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Detalles Bibliográficos
Autores: Granero Belinchón, Rafael|||0000-0003-2752-8086, Hunter, John K
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:francés
OAI Identifier:oai:repositorio.unican.es:10902/29547
Acceso en línea:https://hdl.handle.net/10902/29547
Access Level:acceso abierto
Palabra clave:Kuramoto-Sivashinsky equation
Spatial chaos
Attractor
Descripción
Sumario: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.