Relaxation rates for a perturbation of a stationary solution to the thin-film equation
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Submission date: 20. Apr. 2015
published in: SIAM journal on mathematical analysis, 48 (2016) 1, p. 349-396
DOI number (of the published article): 10.1137/15M1017697
MSC-Numbers: 35B40, 35K25, 35K55, 35K65, 35Q35
Keywords and phrases: thin-film equation, stability of solutions, gradient flow
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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.