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Modelling and Analysis of Nonnecrotic Tumors: a Functional Analytic Approach
Anca-voichita Matioc
Modelling and Analysis of Nonnecrotic Tumors: a Functional Analytic Approach
Anca-voichita Matioc
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 principle of 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.
Mídia | Livros Paperback Book (Livro de capa flexível e brochura) |
Lançado | 25 de junho de 2010 |
ISBN13 | 9783838113241 |
Editoras | Südwestdeutscher Verlag für Hochschulsch |
Páginas | 140 |
Dimensões | 225 × 8 × 150 mm · 227 g |
Idioma | German |
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