Bifurcation Analysis of an Elliptic Free Boundary Problem Modelling the Growth of Avascular Tumors
Shangbin Cui, Joachim Escher · SIAM Journal on Mathematical Analysis · 2007
We study bifurcations from radially symmetric solutions of a free boundary problem modelling the dormant state of nonnecrotic avascular tumors. This problem consists of two semilinear elliptic equations with a Dirichlet and a Neumann boundary condition, respectively, and a third boundary condition coupling surface tension effects on the free interface to the internal pressure. By reducing the full problem to an abstract bifurcation equation in terms of the free boundary only and by characterizing the linearization as a Fourier multiplication operator, we carry out a precise analysis of local bifurcations of this problem.