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May/June 2010 Surface diffusion with triple junctions: A stability criterion for stationary solutions
Harald Garcke, Kazuo Ito, Yoshihito Kohsaka
Adv. Differential Equations 15(5/6): 437-472 (May/June 2010).

Abstract

We study a fourth-order geometric evolution problem on a network of curves in a bounded domain $\Omega$. The flow decreases a weighted total length of the curves and preserves the enclosed volumes. Stationary solutions of the flow are critical points of a partition problem in $\Omega$. In this paper we study the linearized stability of stationary solutions using the $H^{-1}$-gradient flow structure of the problem. Important issues are the development of an appropriate PDE formulation of the geometric problem and Poincaré type estimate on a network of curves.

Citation

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Harald Garcke. Kazuo Ito. Yoshihito Kohsaka. "Surface diffusion with triple junctions: A stability criterion for stationary solutions." Adv. Differential Equations 15 (5/6) 437 - 472, May/June 2010.

Information

Published: May/June 2010
First available in Project Euclid: 18 December 2012

zbMATH: 1228.35042
MathSciNet: MR2643231

Subjects:
Primary: 35B35, 35G30, 35K55, 35R35, 53C44

Rights: Copyright © 2010 Khayyam Publishing, Inc.

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Vol.15 • No. 5/6 • May/June 2010
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