Global Solution to the Allen-cahn Equation with Singular Potentials and Dynamic Boundary Conditions

We prove well-posedness results for the solution to an initial and boundaryvalue problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic boundary conditions for the order parameter have been recently proposed by some physicists to account for interactions with the walls (see [14] and [20]). We show our results using suitable regularizations of the nonlinearities of the problem and performing some a priori estimates which allow us to pass to the limit thanks to compactness and monotonicity arguments. ————————————————————–