Geodesic
On a phase-field model with a logarithmic nonlinearity
Applications of Mathematics, Tome 57 (2012) no. 3, pp. 215-229.

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Our aim in this paper is to study the existence of solutions to a phase-field system based on the Maxwell-Cattaneo heat conduction law, with a logarithmic nonlinearity. In particular, we prove, in one and two space dimensions, the existence of a solution which is separated from the singularities of the nonlinear term.
DOI : 10.1007/s10492-012-0014-y
Classification : 35A01, 35J60, 35K55, 35K91, 35L10, 35M33, 80A22
Keywords: phase field system; Maxwell-Cattaneo law; well-posedness; logarithmic potential 
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Miranville, Alain. On a phase-field model with a logarithmic nonlinearity. Applications of Mathematics, Tome 57 (2012) no. 3, pp. 215-229. doi : 10.1007/s10492-012-0014-y. http://geodesic.mathdoc.fr/articles/10.1007/s10492-012-0014-y/

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