Well--posedness and asymptotic behaviour for a non-classical and non-autonomous diffusion equation with delay
In this paper, it is analyzed a non-classical non-autonomous di_usion equation with delay. First, the well-posedness and the existence of a local solution is proved by using a _xed point theorem. Then, the existence of solutions de_ned globally in future is ensured. The asymptotic behaviour of solut...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/32727 |
| Acceso en línea: | http://hdl.handle.net/11441/32727 https://doi.org/10.1142/S0218127415400210 |
| Access Level: | acceso abierto |
| Palabra clave: | Delay equations pullback attractors non-autonomous problems evolution processes non-classical di usion equations |
| Sumario: | In this paper, it is analyzed a non-classical non-autonomous di_usion equation with delay. First, the well-posedness and the existence of a local solution is proved by using a _xed point theorem. Then, the existence of solutions de_ned globally in future is ensured. The asymptotic behaviour of solutions is analyzed within the framework of pullback attractors as it has revealed a powerful theory to describe the dynamics of non-autonomous dynamical systems. One di_culty in the case of delays concerns the phase space that one needs to consider to construct the evolution process. This yields to the necessity of using a version of the Ascoli-Arzel_a theorem to prove the compactness. |
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