`a`
Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Stability criteria for multiphase partitioning problems with volume constraints

Pages: 663 - 683, Volume 37, Issue 2, February 2017      doi:10.3934/dcds.2017028

 
       Abstract        References        Full Text (554.3K)       Related Articles       

N. Alikakos - Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece (email)
A. Faliagas - Department of Mathematics, University of Athens, Panepistemiopolis, 15784 Athens, Greece (email)

Abstract: We study the stability of partitions involving two or more phases in convex domains under the assumption of at most two-phase contact, thus excluding in particular triple junctions. We present a detailed derivation of the second variation formula with particular attention to the boundary terms, and then study the sign of the principal eigenvalue of the Jacobi operator. We thus derive certain stability criteria, and in particular we recapture the Sternberg-Zumbrun result on the instability of the disconnected phases in the more general setting of several phases.

Keywords:  Phase partitioning, stability, stability criteria, area functional, second variation.
Mathematics Subject Classification:  Primary: 35B35, 35B36, 49R05; Secondary: 53Z05.

Received: June 2015;      Revised: February 2016;      Available Online: November 2016.

 References