Modelling and analysis of nonnecrotic tumors - Matioc, Anca-Voichita
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Modelling and simulation of tumor growth is one of the challenging frontiers of applied mathematics. We study in this work a mathematical model for the growth of nonnecrotic tumors in different regimes of vascularisation. The tumor is treated as an incompressible fluid, tissue elasticity is neglected, and the mathematical model is a moving boundary problem. In the radially symmetric case we establish the existence of a unique radially symmetric stationary solution and show, that if the initial tumor is radially symmetric, there exists a unique radially symmetric solution of the problem, which…mehr

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Produktbeschreibung
Modelling and simulation of tumor growth is one of the challenging frontiers of applied mathematics. We study in this work a mathematical model for the growth of nonnecrotic tumors in different regimes of vascularisation. The tumor is treated as an incompressible fluid, tissue elasticity is neglected, and the mathematical model is a moving boundary problem. In the radially symmetric case we establish the existence of a unique radially symmetric stationary solution and show, that if the initial tumor is radially symmetric, there exists a unique radially symmetric solution of the problem, which exists for all times. The asymptotic behaviour of this solution it is also discussed. If we consider star-shaped initial tumor domains, we can re-express the mathematical model as an abstract evolution equation. Using general results for parabolic equations we prove the well-posedness of the model. The stability properties of the radially symmetric equilibrium are studied using the principleof linearised stability . Finally, we show, via a bifurcation argument, that there exist also other stationary solutions of the problem, which are no longer radially symmetric.
Autorenporträt
Anca-Voichita Matioc was born in Satu Mare (Romania) in 1980.She graduated mathematics at the West University of Timisoara.During her master study she was one year in Saarbrücken via anErasmus scholarship. She got a scholarship in DFG ResearchTraining Group 615 at the Leibniz University Hanover, where shedefended 2009 her PhD Thesis.