Dipartimento di Matematica ''F. Casorati''

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A diffuse interface tumour model with chemotaxis and active transport

Prof. Kei-Fong Lam, University of Regensburg

Sala Conferenze IMATI-CNR - Giovedì 17 Dicembre 2015 h.16:00

Abstract.  We consider a thermodynamically consistent diffuse interface model for
tumour growth, which couples a Cahn-Hilliard system and a
reaction-diffusion equation. The system of PDEs models the growth of a
tumour in the presence of a nutrient and surrounded by host tissue. A new
feature of the model is the inclusion of transport mechanisms such as
chemotaxis and active transport through specific choices of the fluxes. We
will first discuss a simplified model and derive some results regarding the
well-posedness of the system. Then, we will discuss the more general
model, which is a Cahn-Hilliard-Darcy system coupled to a
convection-reaction-diffusion equation for the nutrient. The effects of
including the transport mechanisms and fluid flow will be demonstrated with
numerical computations, and if time permitting, we will discuss some recent
results regarding the existence of weak solutions to the general model.

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Dipartimento di Matematica ''F. Casorati''

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