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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Symmetry-breaking bifurcation of analytic solutions to free boundary problems: An application to a model of tumor growth


Authors: Avner Friedman and Fernando Reitich
Journal: Trans. Amer. Math. Soc. 353 (2001), 1587-1634
MSC (1991): Primary 35B32, 35R35; Secondary 35B30, 35B60, 35C10, 35J85, 35Q80, 92C15, 95C15
Published electronically: November 21, 2000
MathSciNet review: 1806728
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we develop a general technique for establishing analyticity of solutions of partial differential equations which depend on a parameter $\varepsilon$. The technique is worked out primarily for a free boundary problem describing a model of a stationary tumor. We prove the existence of infinitely many branches of symmetry-breaking solutions which bifurcate from any given radially symmetric steady state; these asymmetric solutions are analytic jointly in the spatial variables and in $\varepsilon$.


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Additional Information

Avner Friedman
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: friedman@math.umn.edu

Fernando Reitich
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: reitich@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02715-X
PII: S 0002-9947(00)02715-X
Keywords: Free boundary problem, steady states, bifurcation, symmetry-breaking, analytic solutions, tumor growth
Received by editor(s): August 17, 1999
Published electronically: November 21, 2000
Article copyright: © Copyright 2000 American Mathematical Society