Abstract. Our aim, in this paper, is to study a generalization of the Caginalp phase-field system based on the Gurtin-Pipkin law with two temperatures for heat conduction with memory. In particular, we obtain well-posedness results and study the dissipativity, in terms of the global attractor with optimal regularity, of the associated solution operators. We also study the stability of the system as the memory kernel collapses to a Dirac mass.
A phase-field system with two temperatures and memory / Conti, Monica; Gatti, Stefania; Miranville, Alain. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - ELETTRONICO. - 30:1-2(2017), pp. 53-80.
A phase-field system with two temperatures and memory
GATTI, Stefania;
2017
Abstract
Abstract. Our aim, in this paper, is to study a generalization of the Caginalp phase-field system based on the Gurtin-Pipkin law with two temperatures for heat conduction with memory. In particular, we obtain well-posedness results and study the dissipativity, in terms of the global attractor with optimal regularity, of the associated solution operators. We also study the stability of the system as the memory kernel collapses to a Dirac mass.
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