Convergence of solutions for the fractional Cahn-Hilliard system
Analysis of PDEs
2018-01-08 v1
Abstract
This paper deals with the Cauchy-Dirichlet problem for the fractional Cahn-Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called \L ojasiewicz-Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but ) nonlinearities.
Keywords
Cite
@article{arxiv.1801.01722,
title = {Convergence of solutions for the fractional Cahn-Hilliard system},
author = {Goro Akagi and Giulio Schimperna and Antonio Segatti},
journal= {arXiv preprint arXiv:1801.01722},
year = {2018}
}