Journal of Differential Geometry

Nonlinear stability results for the modified Mullins–Sekerka and the surface diffusion flow

E. Acerbi, N. Fusco, V. Julin, and M. Morini

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Abstract

It is shown that any three-dimensional periodic configuration that is strictly stable for the area functional is exponentially stable for the surface diffusion flow and for the Mullins–Sekerka or Hele–Shaw flow. The same result holds for three-dimensional periodic configurations that are strictly stable with respect to the sharp-interface Ohta–Kawaski energy. In this case, they are exponentially stable for the so-called modified Mullins–Sekerka flow.

Article information

Source
J. Differential Geom., Volume 113, Number 1 (2019), 1-53.

Dates
Received: 14 June 2016
First available in Project Euclid: 31 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1567216953

Digital Object Identifier
doi:10.4310/jdg/1567216953

Mathematical Reviews number (MathSciNet)
MR3998906

Zentralblatt MATH identifier
07104702

Keywords
Mullins–Sekerka flow Hele–Shaw flow Ohta–Kawaski energy gradient flows asymptotic stability global-in-time existence large-time behavior stable periodic structures

Citation

Acerbi, E.; Fusco, N.; Julin, V.; Morini, M. Nonlinear stability results for the modified Mullins–Sekerka and the surface diffusion flow. J. Differential Geom. 113 (2019), no. 1, 1--53. doi:10.4310/jdg/1567216953. https://projecteuclid.org/euclid.jdg/1567216953


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