Robust exponential attractors for a family of nonconserved phase-field systems with memory

S. Gatti; M. Grasselli; V. Pata; M. Squassina

doi:10.3934/dcds.2005.12.1019

Article Contents

2005, Volume 12, Issue 5: 1019-1029. Doi: 10.3934/dcds.2005.12.1019

This issue Previous Article The exponential behavior of Navier-Stokes equations with time delay external force Next Article Topology of Sobolev mappings IV

Robust exponential attractors for a family of nonconserved phase-field systems with memory

1.
Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, I-44100 Ferrara
2.
Dipartimento di Matematica "F. Brioschi", Politecnico di Milano, I-20133 Milano
3.
Dipartimento di Matematica "F.Brioschi", Politecnico di Milano, Via Bonardi 9, I-20133 Milano

Received: February 29, 2004

Revised: October 31, 2004

Published: September 2005

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Abstract

We consider a family of phase-field systems with memory effects in the temperature $\vartheta$, depending on a parameter $\omega\geq 0$. Setting the problems in a suitable phase-space accounting for the past history of $\vartheta$, we prove the existence of a family of exponential attractors $\mathcal E_\omega$ which is robust as $\omega\to 0$.

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Mathematics Subject Classification: 35B40, 35B41, 37L25, 45K05, 80A22.

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