Optimal $L^1$-type relaxation rates for the Cahn-Hilliard equation on the line
Analysis of PDEs
2019-07-11 v2
Abstract
In this paper we derive optimal algebraic-in-time relaxation rates to the kink for the Cahn-Hilliard equation on the line. We assume that the initial data have a finite distance---in terms of either a first moment or the excess mass---to a kink profile and capture the decay rate of the energy and the perturbation. Our tools include Nash-type inequalities, duality arguments, and Schauder estimates.
Keywords
Cite
@article{arxiv.1806.02519,
title = {Optimal $L^1$-type relaxation rates for the Cahn-Hilliard equation on the line},
author = {Felix Otto and Sebastian Scholtes and Maria G. Westdickenberg},
journal= {arXiv preprint arXiv:1806.02519},
year = {2019}
}