Advances in Differential Equations

Instability of spherical interfaces in a nonlinear free boundary problem

X. Chen and M. Taniguchi

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Existence and stability of spherically symmetric stationary interfaces in a two-phase boundary problem are studied in ${\bf R}^{N}$ $(N \geq 2)$. We show that there exist two such solutions: a large ball and a small one. The linearized eigenvalue problem shows that the large ball is unstable with some fastest growing mode. We specify the mode precisely.

Article information

Adv. Differential Equations, Volume 5, Number 4-6 (2000), 747-772.

First available in Project Euclid: 27 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems
Secondary: 35B35: Stability 92B05: General biology and biomathematics


Chen, X.; Taniguchi, M. Instability of spherical interfaces in a nonlinear free boundary problem. Adv. Differential Equations 5 (2000), no. 4-6, 747--772.

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