Generalized Allen-Cahn and Cahn-Hilliard equations with p-Laplacian in 1-d

In this talk, I consider some generalizations of the classical Allen-Cahn and Cahn-Hilliard models in a bounded interval of the real line with no-flux boundary conditions. In particular, the linear diffusion (typical of the classical models) is replaced by the (nonlinear) p-Laplace operator and the reaction term is the derivative of a double well potential with wells of equal depth. After investigating the associated stationary problem and highlighting the differences with the standard results, we focus the attention on the long time dynamics of solutions, proving either exponentially or algebraic slow motion of profiles with a transition layer structure. This is a joint work with Luis López Ríos (IIMAS-UNAM), Ramón Plaza
(IIMAS-UNAM) and Marta Strani (University of Venice).