Dynamics in dumbbell domains III. Continuity of attractors
In this paper we conclude the analysis started in [3] and continued in [4] con- cerning the behavior of the asymptotic dynamics of a dissipative reactions di_usion equation in a dumbbell domain as the channel shrinks to a line segment. In [3], we have established an appropriate functional analytic f...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/42008 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/42008 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.9 Hyperbolic equilibria Shrinking channels Lower semicontinuous Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
| Sumario: | In this paper we conclude the analysis started in [3] and continued in [4] con- cerning the behavior of the asymptotic dynamics of a dissipative reactions di_usion equation in a dumbbell domain as the channel shrinks to a line segment. In [3], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [4], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in Lp and H1 norms |
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