ATTRACTORS FOR A CAGINALP MODEL WITH A LOGARITHMIC POTENTIAL AND COUPLED DYNAMIC BOUNDARY CONDITIONS

We study the longtime behavior of the Caginalp phase-field model with a logarithmic potential and dynamic boundary conditions for both the order parameter and the temperature. Due to the possible lack of distributional solutions, we deal with a suitable definition of solutions based on variational inequalities, for which we prove well-posedness and the existence of global and exponential attractors with finite fractal dimension.

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