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 . 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 .

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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:
https://doi.org/10.1090/S0002-9947-00-02715-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