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MiS Preprint
27/2015

Relaxation rates for a perturbation of a stationary solution to the thin-film equation

Elias Esselborn

Abstract

In this work we study the stability of a stationary solution to the thin-film equation with linear mobility and partial wetting boundary conditions. The method used is strongly based on the gradient-flow structure of the problem. We obtain natural relaxation rates of perturbations to the stationary solution by showing that the energy is in fact convex in a neighborhood around the stationary solution.

Received:
20.04.15
Published:
21.04.15
MSC Codes:
35B40, 35K25, 35K55, 35K65, 35Q35
Keywords:
thin-film equation, stability of solutions, gradient flow

Related publications

inJournal
2016 Repository Open Access
Elias Esselborn

Relaxation rates for a perturbation of a stationary solution to the thin-film equation

In: SIAM journal on mathematical analysis, 48 (2016) 1, pp. 349-396