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Více informací o knize Modelling and Analysis of Nonnecrotic Tumors

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• Anotace
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Anotace knihy

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.

Parametry knihy

Zařazení knihy Knihy v angličtině Mathematics & science Mathematics

• Plný název: Modelling and Analysis of Nonnecrotic Tumors
• Autor: Anca-Voichita Matioc
• Jazyk: Angličtina
• Vazba: Brožovaná
• Počet stran: 140
• EAN: 9783838113241
• ISBN: 3838113241
• ID: 07006938
• Nakladatelství: Sudwestdeutscher Verlag Fur Hochschulschriften AG
• Hmotnost: 213 g
• Rozměry: 229 × 152 × 9 mm
• Datum vydání: 25. June 2010

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