Well-posedness and stability analysis for a moving boundary problem modelling the growth of nonnecrotic tumors

Pages: 573 - 596, Volume 15, Issue 3, May 2011

doi:10.3934/dcdsb.2011.15.573       Abstract        References        Full Text (498.7K)       Related Articles

Joachim Escher - Institute for Applied Mathematics, Leibniz University Hanover, Welfengarten 1, 30167 Hanover, Germany (email)
Anca-Voichita Matioc - Institute for Applied Mathematics, Leibniz University Hanover, Welfengarten 1, 30167 Hanover, Germany (email)

Abstract: We study a moving boundary problem describing the growth of nonnecrotic tumors in different regimes of vascularisation. This model consists of two decoupled Dirichlet problem, one for the rate at which nutrient is added to the tumor domain and one for the pressure inside the tumor. These variables are coupled by a relation which describes the dynamic of the boundary. By re-expressing the problem as an abstract evolution equation, we prove local well-posedness in the small Hölder spaces context. Further on, we use the principle of linearised stability to characterise the stability properties of the unique radially symmetric equilibrium of the problem.

Keywords:  Tumor growth, Moving boundary problem, Well-posedness, Stability.
Mathematics Subject Classification:  Primary: 35B35; Secondary: 35B40, 35K55.

Received: February 2010;      Revised: April 2010;      Published: February 2011.

 References