On a Caginalp phase-field system with a logarithmic nonlinearity. (English) Zbl 1363.35045

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.


35B40 Asymptotic behavior of solutions to PDEs
35B41 Attractors
35K51 Initial-boundary value problems for second-order parabolic systems
80A22 Stefan problems, phase changes, etc.
80A20 Heat and mass transfer, heat flow (MSC2010)
35Q53 KdV equations (Korteweg-de Vries equations)
45K05 Integro-partial differential equations
35K55 Nonlinear parabolic equations
35G30 Boundary value problems for nonlinear higher-order PDEs
92D50 Animal behavior
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