Symmetry‐breaking bifurcations of free boundary problems in three dimensions

Article type: Research Article

Authors: Fontelos, Marco A. | Friedman, Avner

Affiliations: Departamento de Matemática Aplicada, Universidad Rey Juan Carlos, C/ Tulipán S/N, 28933 Móstoles, Madrid, Spain E‐mail: [email protected] | Department of Mathematics, The Ohio State University, 231, 18th Ave. W, Columbus, OH 43210, USA E‐mail: [email protected]‐state.edu

Abstract: In this paper we consider free boundary problems for systems of partial differential equations. The system has solutions which are spherically symmetric with free boundary r=R, for any value of a parameter γ. We establish the existence of symmetry‐breaking bifurcation branches of solutions with free boundary of the form r=R+εF.

Keywords: free boundary problem, steady states, bifurcation, symmetry‐breaking, tumor growth

Journal: Asymptotic Analysis, vol. 35, no. 3-4, pp. 187-206, 2003