Attractors for a Caginalp Phase-Field Model with Singular Potential (Journal of Mathematical Study, 2021)
We consider a phase field model based on a generalization of the MaxwellCattaneo heat conduction law, with a logarithmic nonlinearity, associated with Neumann boundary conditions. The originality here, compared with previous works, isthat we obtain global in time and dissipative estimates, so that, in particular, we prove,in one and two space dimensions, the existence of a unique solution which is strictlyseparated from the singularities of the nonlinear term, as well as the existence of thefinite-dimensional global attractor and of exponential attractors. In three space dimensions, we prove the existence of a solution.