Extremal equilibria for reaction-diffusion equations in bounded domains and applications
We show the existence of two special equilibria, the extremal ones, for a wide class of reaction–diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and so for the attractor. Some results on the existence an...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2008 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/49703 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/49703 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.9 Reaction-diffusion equation Extremal equilibria Attractor Nonlinear boundary conditions Dirichlet boundary condition Robin boundary condition Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
| Sumario: | We show the existence of two special equilibria, the extremal ones, for a wide class of reaction–diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and so for the attractor. Some results on the existence and/or uniqueness of positive solutions are also obtained. As a consequence, several well-known results on the existence and/or uniqueness of solutions for elliptic equations are revisited in a unified way obtaining, in addition, information on the dynamics of the associated parabolic problem. Finally, we ilustrate the use of the general results by applying them to the case of logistic equations. In fact, we obtain a detailed picture of the positive dynamics depending on the parameters appearing in the equation |
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