Approximating travelling waves by equilibria of non-local equations
We consider an evolution equation of parabolic type in R having a travelling wave solution. We study the effects on the dynamics of an appropriate change of variables which transforms the equation into a non-local evolution one having a travelling wave solution with zero speed of propagation with ex...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/569 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/569 |
| Access Level: | acceso abierto |
| Palabra clave: | asymptotic stability implicit coordinate-change non-local equation numerical approximation reaction-diffusion equations travelling waves |
| Sumario: | We consider an evolution equation of parabolic type in R having a travelling wave solution. We study the effects on the dynamics of an appropriate change of variables which transforms the equation into a non-local evolution one having a travelling wave solution with zero speed of propagation with exactly the same profile as the original one. This procedure allows us to compute simultaneously the travelling wave profile and its propagation speed avoiding moving meshes, as we illustrate with several numerical examples. We analyze the relation of the new equation with the original one in the entire real line. We also analyze the behavior of the non-local problem in a bounded interval with appropriate boundary conditions. We show that it has a unique stationary solution which approaches the traveling wave as the interval gets larger and larger and that is asymptotically stable for large enough intervals. |
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