Differential and Integral Equations

A phase-field system with two temperatures and memory

Monica Conti, Stefania Gatti, and Alaine Miranville

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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.

Article information

Differential Integral Equations, Volume 30, Number 1/2 (2017), 53-80.

First available in Project Euclid: 20 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35B41: Attractors 35K55: Nonlinear parabolic equations 35L05: Wave equation 80A22: Stefan problems, phase changes, etc. [See also 74Nxx]


Conti, Monica; Gatti, Stefania; Miranville, Alaine. A phase-field system with two temperatures and memory. Differential Integral Equations 30 (2017), no. 1/2, 53--80. https://projecteuclid.org/euclid.die/1484881219

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