On a Caginalp phase-field system with a logarithmic nonlinearity

[摘要] 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.

[学科分类] 应用数学

[关键词] Caginalp phase-field system;Dirichlet boundary conditions;well-posedness;long time behavior of solution;global attractor;exponential attractor;Maxwell-Cattaneo law;logarithmic potential