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...

Descripción completa

Detalles Bibliográficos
Autores: Belluzi, Maykel, Caraballo Garrido, Tomás, Nascimento, Marcelo J.D., Schiabel, Karina
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
Descripción
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.