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 - <p style="text-align: justify;">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.</p>