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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 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.
| Autorius: | Anca-Voichita Matioc |
| Leidėjas: | Südwestdeutscher Verlag für Hochschulschriften AG Co. KG |
| Išleidimo metai: | 2015 |
| Knygos puslapių skaičius: | 140 |
| ISBN-10: | 3838113241 |
| ISBN-13: | 9783838113241 |
| Formatas: | 220 x 150 x 9 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Modelling and analysis of nonnecrotic tumors: A Functional Analytic Approach“
