Advances in Differential Equations

Instability of spherical interfaces in a nonlinear free boundary problem

X. Chen and M. Taniguchi

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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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1356651346

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.


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