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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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:
Apr 20, 2015
Published:
Apr 21, 2015
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