The singular limit of

a vector-valued reaction-diffusion process

Authors:
Lia Bronsard and Barbara Stoth

Journal:
Trans. Amer. Math. Soc. **350** (1998), 4931-4953

MSC (1991):
Primary 35B25, 35K57

DOI:
https://doi.org/10.1090/S0002-9947-98-02020-0

MathSciNet review:
1443865

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the asymptotic behaviour of the solution to the vector-valued reaction-diffusion equation

where . We assume that the the potential depends only on the modulus of and vanishes along two concentric circles. We present a priori estimates for the solution , and, in the spatially radially symmetric case, we show rigorously that in the singular limit as , two phases are created. The interface separating the bulk phases evolves by its mean curvature, while evolves according to a harmonic map flow on the respective circles, coupled across the interfaces by a jump condition in the gradient.

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Additional Information

**Lia Bronsard**

Affiliation:
Department of Mathematics, McMaster University, Hamilton, Ont. L8S 4K1, Canada

Email:
bronsard@math.mcmaster.ca

**Barbara Stoth**

Affiliation:
IAM, Universität Bonn, 53115 Bonn, Deutschland

Email:
bstoth@iam.uni-bonn.de

DOI:
https://doi.org/10.1090/S0002-9947-98-02020-0

Received by editor(s):
November 17, 1995

Received by editor(s) in revised form:
October 15, 1996

Article copyright:
© Copyright 1998
American Mathematical Society