A Caginalp phase-field system based on type III heat conduction with two temperatures

Miranville, Alain; Quintanilla, Ramon

doi:10.1090/qam/1430

Authors: Alain Miranville and Ramon Quintanilla
Journal: Quart. Appl. Math. 74 (2016), 375-398
MSC (2010): Primary 35K55, 35J60, 80A22
DOI: https://doi.org/10.1090/qam/1430
Published electronically: March 16, 2016
MathSciNet review: 3505609
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Abstract: Our aim in this paper is to study a generalization of the Caginalp phase-field system based on the theory of type III thermomechanics with two temperatures for the heat conduction. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators. We consider here both regular and singular nonlinear terms. Furthermore, we endow the equations with two types of boundary conditions, namely, Dirichlet and Neumann. Finally, we study the spatial behavior of the solutions in a semi-infinite cylinder, when such solutions exist.

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