Long-Time Behavior for Semilinear Equation with Time-Dependent and Almost Sectorial Linear Operator
In this paper we study the solvability and asymptotic dynamics of a nonautonomous semilinear reaction–diffusion equation in a domain with a handle Ωo = Ω U Ro, formed by an open subset Ω C RN connected to a line segment Ro at the ending points of the segment. We also assume that the linear part of t...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/183376 |
| Acceso en línea: | https://hdl.handle.net/11441/183376 https://doi.org/10.1007/s10884-024-10378-3 |
| Access Level: | acceso abierto |
| Palabra clave: | Semilinear problem Almost sectorial operators Time-dependent linear operator Pullback attractor |
| Sumario: | In this paper we study the solvability and asymptotic dynamics of a nonautonomous semilinear reaction–diffusion equation in a domain with a handle Ωo = Ω U Ro, formed by an open subset Ω C RN connected to a line segment Ro at the ending points of the segment. We also assume that the linear part of this equation (the diffusion term) is time-dependent and the growth condition on the nonlinearity F is more general than linear growth. o obtain existence of local solution, the uniformly almost sectoriality of the family of linear operator associated to the evolution equation is explored. An abstract result on existence of mild solution for semilinear problems of the form. |
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