Garcke, Harald and Ito, Kazuo and Kohsaka, Yoshihito
Surface diffusion with triple junctions: A stability criterion for stationary solutions.
Advances in Differential Equations 15 (5-6), pp. 437-472.
We study a fourth order geometric evolution problem on a network of curves
in a bounded domain
. 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
. 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 Poincar´e
type estimate on a network of curves.
|Institutions:|| Mathematics > Prof. Dr. Harald Garcke|
|Keywords:||fourth order geometric evolution problem, surface diffusion, network of
curves, linearized stability, Poincar´e inequality on a network, H−1-gradient flow
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Partially|
|Deposited On:||24 Mar 2010 06:46|
|Last Modified:||20 Jul 2011 22:24|