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Bifurcation analysis of amathematical model for the growth of solid tumors in the presence of external inhibitors
Author(s) -
Wu Junde,
Cui Shangbin
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3190
Subject(s) - mathematics , bifurcation , mathematical analysis , boundary (topology) , neumann boundary condition , bifurcation theory , dirichlet boundary condition , surface tension , boundary value problem , nonlinear system , physics , quantum mechanics
We study bifurcations from radial solution of a free boundary problem modeling the dormant state of nonnecrotic solid tumors in the presence of external inhibitors. This problem consists in three linear elliptic equations with two Dirichlet and one Neumann boundary conditions and a fourth boundary condition coupling surface tension effects on free boundary. In this paper, surface tension coefficient γ plays the role of bifurcation parameter. We prove that in certain situations there exists a positive null point sequence for γ where bifurcation occurs from radial solution, while in the other situations, either bifurcation occurs at only finite many points of γ or even it does not occur for any γ > 0. Copyright © 2014 John Wiley & Sons, Ltd.