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arXiv · 1806.02519

Optimal $L^1$-type relaxation rates for the Cahn-Hilliard equation on the line

Felix Otto·Sebastian Scholtes·Maria G. Westdickenberg
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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.

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Felix Otto, Sebastian Scholtes, Maria G. Westdickenberg. 2018-06-07. Optimal $L^1$-type relaxation rates for the Cahn-Hilliard equation on the line. https://arxiv.org/abs/1806.02519

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