Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations
It is well-known that the existence of traveling wave solutions for reaction-diffusion partial differential equations can be proved by showing the existence of certain heteroclinic orbits for related autonomous planar differential equations. We introduce a method for finding explicit upper and lower...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150651 |
| Acceso en línea: | https://ddd.uab.cat/record/150651 https://dx.doi.org/urn:doi:10.3934/dcds.2013.33.3567 |
| Access Level: | acceso abierto |
| Palabra clave: | Traveling wave Heteroclinic orbit Fisher-Kolmogorov equation Reaction-diffusion partial differential equation Invariant manifold |
| Sumario: | It is well-known that the existence of traveling wave solutions for reaction-diffusion partial differential equations can be proved by showing the existence of certain heteroclinic orbits for related autonomous planar differential equations. We introduce a method for finding explicit upper and lower bounds of these heteroclinic orbits. In particular, for the classical Fisher-Kolmogorov equation we give rational upper and lower bounds which allow to locate these solutions analytically and with very high accuracy. |
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