Transactions of the American Mathematical Society

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

Author(s): Avner Friedman; Fernando Reitich
Journal: Trans. Amer. Math. Soc. 353 (2001), 1587-1634.
MSC (1991): Primary 35B32, 35R35; Secondary 35B30, 35B60, 35C10, 35J85, 35Q80, 92C15, 95C15
Posted: November 21, 2000
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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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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: 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
Posted: November 21, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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