TY - JOUR T1 - Attractors for a Caginalp Phase-Field Model with Singular Potential AU - Miranville , Alain AU - Wehbe , Charbel JO - Journal of Mathematical Study VL - 4 SP - 337 EP - 376 PY - 2018 DA - 2018/12 SN - 51 DO - http://doi.org/10.4208/jms.v51n4.18.01 UR - https://global-sci.org/intro/article_detail/jms/12915.html KW - Caginalp phase-field system, Maxwell-Cattaneo law, logarithmic potential, Neumann boundary conditions, well-posedness, global attractor, exponential attractor. AB -

We consider a phase field model based on a generalization of the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Neumann boundary conditions. The originality here, compared with previous works, is that 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 strictly separated from the singularities of the nonlinear term, as well as the existence of the finite-dimensional global attractor and of exponential attractors. In three space dimensions, we prove the existence of a solution.