Archive for Rational Mechanics and Analysis

, Volume 180, Issue 2, pp 293–330

Bifurcation From Stability to Instability for a Free Boundary Problem Arising in a Tumor Model

Article

Abstract

We consider a time-dependent free boundary problem with radially symmetric initial data: σt − Δσ + σ = 0 if Open image in new window and σ(r,0)=σ0(r) in {r < R(0)} where R(0) is given. This is a model for tumor growth, with nutrient concentration (or tumor cells density) σ(r,t) and proliferation rate Open image in new window then there exists a unique stationary solution (σS(r), RS), where RS depends only on the number Open image in new window. We prove that there exists a number μ*, such that if μ < μ* . . . then the stationary solution is stable with respect to non-radially symmetric perturbations, whereas if μ > μ* then the stationary solution is unstable.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA
  2. 2.Department of MathematicsUniversity of Notre DameIndiana

Personalised recommendations