Non-isothermal Allen-Cahn equations with dynamic boundary conditions
by
Ciprian G. Gal
University of Missouri, Columbia
Coauthors: Maurizio Grasselli and Alain Miranville

We consider a phase-field system of Caginalp type on a three-dimensional bounded domain. The order parameter fulfills a nonlinear dynamic boundary condition, while the (relative) temperature is subject to a boundary condition of Dirichlet, Neumann, Robin or dynamic (Wentzell) type. The corresponding class of initial and boundary value problems has already been studied by us and few others, proving well-posedness results and the existence of global attractors as well as exponential attractors. We intend to discuss recent new results and improvements over the previous analysis. We also demonstrate that each trajectory converges to a single equilibrium by means of a Łojasiewicz-Simon type inequality. We also obtain a convergence rate estimate.

Date received: March 4, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawu-82.