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

Joachim Escher; Anca-Voichita Matioc

doi:10.3934/dcdsb.2011.15.573

Article Contents

2011, Volume 15, Issue 3: 573-596. Doi: 10.3934/dcdsb.2011.15.573

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

Joachim Escher^1, and
Anca-Voichita Matioc^1,

1.
Institute for Applied Mathematics, Leibniz University Hanover, Welfengarten 1, 30167 Hanover

Received: January 31, 2010

Revised: March 31, 2010

Published: September 2011

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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.

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Mathematics Subject Classification: Primary: 35B35; Secondary: 35B40, 35K55.

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