Abstract |
In this research project we investigate the evolution of tumor growth
relying on a non-linear model of partial differential equations which
incorporates mechanical laws for tissue compression combined with rules for
nutrients availability and drug application. Rigorous analysis and
simulations are presented which show the role of nutrient and drug
application in the evolution of cancerous cells. We construct a numerical
scheme to approximate solutions of the nonlinear system and establish its
convergence by employing compactness methods in the spirit of P.L. Lions.
Extensive numerical tests show that solutions exhibit a necrotic core when
the nutrient level falls below a critical level in accordance with medical
observations. The talk will present results obtained in collaboration with
D. Donatelli and F. Weber.
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