Geodesic
On a Caginalp phase-field system with a logarithmic nonlinearity
Applications of Mathematics, Tome 60 (2015) no. 4, pp. 355-382.

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We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.
DOI : 10.1007/s10492-015-0101-y
Classification : 35B40, 35B41, 35G30, 35K51, 35K55, 35Q53, 45K05, 80A20, 80A22, 92D50
Keywords: Caginalp phase-field system; Dirichlet boundary conditions; well-posedness; long time behavior of solution; global attractor; exponential attractor; Maxwell-Cattaneo law; logarithmic potential 
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Wehbe, Charbel. On a Caginalp phase-field system with a logarithmic nonlinearity. Applications of Mathematics, Tome 60 (2015) no. 4, pp. 355-382. doi : 10.1007/s10492-015-0101-y. http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0101-y/

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