Global attractor for a non-autonomous integro-differential equation in materials with memory

The long-time behavior of an integro-differential parabolic equation of diffusion type with memory terms, expressed by convolution integrals involving infinite delays and by a forcing term with bounded delay, is investigated in this paper. The assumptions imposed on the coefficients are weak in the...

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Detalles Bibliográficos
Autores: Caraballo Garrido, Tomás, Garrido Atienza, María José, Schmalfuss, Björn, Valero Cuadra, José
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/23670
Acceso en línea:http://hdl.handle.net/11441/23670
https://doi.org/10.1016/j.na.2010.03.012
Access Level:acceso abierto
Palabra clave:Delayed reaction-diffusion equations
integro-differential equations with memory
non-autonomous (pullback) attractors
multivalued dynamical systems
asymptotic behavior
Descripción
Sumario:The long-time behavior of an integro-differential parabolic equation of diffusion type with memory terms, expressed by convolution integrals involving infinite delays and by a forcing term with bounded delay, is investigated in this paper. The assumptions imposed on the coefficients are weak in the sense that uniqueness of solutions of the corresponding initial value problems cannot be guaranteed. Then, it is proved that the model generates a multivalued non–autonomous dynamical system which possesses a pullback attractor. First, the analysis is carried out with an abstract parabolic equation. Then, the theory is applied to the particular integro-differential equation which is the objective of this paper. The general results obtained in the paper are also valid for other types of parabolic equations with memory.