We consider differential systems with memory terms, expressed by convolution integrals, which account for the past history of one or more variables. The aim of this work is to analyze the passage to the singular limit when the memory kernel collapses into a Dirac mass. In particular, we focus on the reactiondiffusion equation with memory, and we discuss the convergence of solutions on finite time-intervals. When enough dissipativity is present, we also establish convergence results of the global and the exponential attractors. Nonetheless, the techniques here devised are quite general, and suitable to be applied to a large variety of models.

Conti, M., Pata, V., Squassina, M., Singular limit of differential systems with memory, <<INDIANA UNIVERSITY MATHEMATICS JOURNAL>>, 2006; 55 (N/A): 169-216 [http://hdl.handle.net/10807/90748]

Singular limit of differential systems with memory

V.; Squassina
Ultimo
2006

Abstract

We consider differential systems with memory terms, expressed by convolution integrals, which account for the past history of one or more variables. The aim of this work is to analyze the passage to the singular limit when the memory kernel collapses into a Dirac mass. In particular, we focus on the reactiondiffusion equation with memory, and we discuss the convergence of solutions on finite time-intervals. When enough dissipativity is present, we also establish convergence results of the global and the exponential attractors. Nonetheless, the techniques here devised are quite general, and suitable to be applied to a large variety of models.
Inglese
Conti, M., Pata, V., Squassina, M., Singular limit of differential systems with memory, <<INDIANA UNIVERSITY MATHEMATICS JOURNAL>>, 2006; 55 (N/A): 169-216 [http://hdl.handle.net/10807/90748]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/90748
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 86
  • ???jsp.display-item.citation.isi??? 72
social impact