Mechanical models of tissue growth are now well settled with continuous inputs from medicine, biology, physics, mechanics and mathematics. They contain several levels of complexity, both in terms of the biomedical content and mathematical description, from ordinary differential equations to sophisticated partial differential equations. They serve to predict the evolution of cancers in medical treatments, to understand the biological effects that permit tumor growth and control by treatment, in some cases, their implication in therapies failure.

Based on the mechanical point of view that a living tissue behaves as a porous medium, this course aims at deriving incompressible, free boundary problems departing from compressible models. The specific questions that will be addressed are: • Aspects of tumor growth modelled by differential equations • Mechanical models of tissue growth • The incompressible limit and the free boundary problems • Models with multiple species, with surface tension

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Presentazione orale

P.D.2-2 - Maggio