Statistical solutions and piecewise Liouville theorem for the impulsive reaction-diffusion equations on in nite lattices
We first verify the global well-posedness of the impulsive reaction-diffusion equations on infinite lattices. Then we establish that the generated process by the solution operators has a pullback attractor and a family of Borel invariant probability measures. Furthermore, we formulate the definition...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/116649 |
| Acceso en línea: | https://hdl.handle.net/11441/116649 https://doi.org/10.1016/j.amc.2021.126103 |
| Access Level: | acceso abierto |
| Palabra clave: | Statistical solution Impulsive lattice system Reaction-diffusion equation Piecewise Liouville theorem Pullback attractor |
| Sumario: | We first verify the global well-posedness of the impulsive reaction-diffusion equations on infinite lattices. Then we establish that the generated process by the solution operators has a pullback attractor and a family of Borel invariant probability measures. Furthermore, we formulate the definition of statistical solution for the addressed impulsive system and prove the existence. Our results show that the statistical solution of the impulsive system satisfies merely the Liouville type theorem piecewise, and the Liouville type equation for impulsive system will not always hold true on the interval containing any impulsive point. |
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