### Instability of spherical interfaces in a nonlinear free boundary problem

#### Abstract

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

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

Dates
First available in Project Euclid: 27 December 2012

Mathematical Reviews number (MathSciNet)
MR1750117

Zentralblatt MATH identifier
1012.35081

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

#### Citation

Chen, X.; Taniguchi, M. Instability of spherical interfaces in a nonlinear free boundary problem. Adv. Differential Equations 5 (2000), no. 4-6, 747--772. https://projecteuclid.org/euclid.ade/1356651346