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
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. https://doi.org/10.57262/ade/1355854677
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