The singular limit of a vectorvalued reactiondiffusion process
Authors:
Lia Bronsard and Barbara Stoth
Journal:
Trans. Amer. Math. Soc. 350 (1998), 49314953
MSC (1991):
Primary 35B25, 35K57
MathSciNet review:
1443865
Fulltext PDF Free Access
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Abstract: We study the asymptotic behaviour of the solution to the vectorvalued reactiondiffusion 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.unibonn.de
DOI:
http://dx.doi.org/10.1090/S0002994798020200
PII:
S 00029947(98)020200
Received by editor(s):
November 17, 1995
Received by editor(s) in revised form:
October 15, 1996
Article copyright:
© Copyright 1998
American Mathematical Society
