ON A GENERALIZED CAHN-HILLIARD MODEL WITH p-LAPLACIAN

A generalized Cahn-Hilliard model in a bounded interval of the real line with no-flux boundary conditions is considered. The label "generalized" refers to the fact that we consider a concentration dependent mobility, the p-Laplace operator with p > 1 and a double well potential of the form F(u) = 1/2 theta vertical bar 1 - u(2)vertical bar(theta) with theta > 1; these terms replace, respectively, the constant mobility, the linear Laplace operator and the C-2 potential satisfying F ''(+/- 1) > 0, which are typical of the standard Cahn-Hilliard model. 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 when theta >= p > 1. In the critical case theta = p > 1, we prove exponentially slow motion of profiles with a transition layer structure, thus extending the well know results of the standard model, where theta = p = 2; conversely, in the supercritical case theta > p > 1, we prove algebraic slow motion of layered profiles.