Fall workshop on nonlinear and nonlocal PDEs

Plenary talk

Cahn-Hilliard Equations on Random Walk Spaces

José M. Mazón

 Mo, 17:10in  Room 520for  50min

Our aim is to study a nonlocal Cahn-Hilliard model (CHE) in the framework of random walk spaces, which includes as particular cases, the CHE on locally finite weighted connected graphs, the CHE determined by finite Markov chains or the Cahn-Hilliard Equations driven by convolution integrable kernels. We consider different transitions for the phase and the chemical potential, and a large class of potentials including obstacle ones. We prove existence and uniqueness of solu- tions in $L^1$ of the Cahn-Hilliard Equation. We also show that the Cahn-Hilliard equation is the gradient flow of the Ginzburg-Landau free energy functional on an appropriate Hilbert space. We finally study the asymptotic behaviour of the solutions.

Joint work with J. Toledo.

 Overview  Program