In this paper we investigate a class of semilinear stochastic Volterra equations which arise in the theory of heat conduction with memory effects, with dissipative nonlinearities and an additive stochastic term which models a rapidly varying external heat source. We first prove that the problem has a unique solution for all times; further, we analyze the asymptotic behavior of the solution and we prove the existence of an ergodic invariant measure.

Asymptotic behavior of a class of nonlinear stochastic heat equations with memory effects

Bonaccorsi, Stefano
Primo
;
Da Prato, Giuseppe
Secondo
;
Tubaro, Luciano
Ultimo
2012-01-01

Abstract

In this paper we investigate a class of semilinear stochastic Volterra equations which arise in the theory of heat conduction with memory effects, with dissipative nonlinearities and an additive stochastic term which models a rapidly varying external heat source. We first prove that the problem has a unique solution for all times; further, we analyze the asymptotic behavior of the solution and we prove the existence of an ergodic invariant measure.
2012
3
Bonaccorsi, Stefano; Da Prato, Giuseppe; Tubaro, Luciano
File in questo prodotto:
File Dimensione Formato  
BoDPT2012.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 292.67 kB
Formato Adobe PDF
292.67 kB Adobe PDF   Visualizza/Apri
UTM_745.pdf

accesso aperto

Tipologia: Pre-print non referato (Non-refereed preprint)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 377.38 kB
Formato Adobe PDF
377.38 kB Adobe PDF Visualizza/Apri

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/11572/91464
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 14
social impact