Optimal L¹-type relaxation rates for the Cahn-Hilliard equation on\n the line

2018/06/07 by Félix Otto, Otto, Felix, Sebastian Scholtes +3
Engineering · Materials Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Solidification and crystal growth phenomena #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1806.02519

openalex publication_date 2018/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we derive optimal algebraic-in-time relaxation rates to the\nkink for the Cahn-Hilliard equation on the line. We assume that the initial\ndata have a finite distance---in terms of either a first moment or the excess\nmass---to a kink profile and capture the decay rate of the energy and the\nperturbation. Our tools include Nash-type inequalities, duality arguments, and\nSchauder estimates.\n

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