Affiliation:
1. Departamento de Análisis Matemático, Universitat de Valencia, Dr. Moliner 50, 46100 Burjassot, Spain
Abstract
In this paper, we study a nonlocal Cahn–Hilliard equation (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 solutions in [Formula: see text] 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 behavior of the solutions.
Funder
Spanish MCIU and FEDER
Conselleria d'Innovació, Universitats, Ciència y Societat Digital
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Analysis