No. 2018.01
Optimal $L^1$-type relaxation rates for the Cahn-Hilliard equation on the line
F. Otto, S. Scholtes, and M. G. Westdickenberg
Subject: Energy-energy-dissipation, nonlinear pde, gradient flow, relaxation rates
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.
Reference
Accepted: SIAM J. Math. Anal.