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Keywords:
Caginalp phase-field system; Dirichlet boundary conditions; well-posedness; long time behavior of solution; global attractor; exponential attractor; Maxwell-Cattaneo law; logarithmic potential
Summary:
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.
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