Tumor growth: From agent-based model to free-boundary problem

Friday, March 16, 2018 - 11:00am to 12:00pm
Location: 
WXLR A106

Speaker

Sebastien Motsch
Assistant Professor
Arizona State University

Abstract

In this talk, we investigate the large time behavior of an agent-based model modeling tumor growth. This microscopic model combines short-range repulsion and cell division. We derive the associated macroscopic dynamics leading to a porous media type equation. In order to capture the long-time behavior of the microscopic model, we have to modify the porous media in order to include a density threshold for the repulsion. The main difficulty is then to investigate the limit as the repulsion between cells becomes singular (modeling non-overlapping constraint). We show formally that such asymptotic limits leads to a free-boundary problem (Hele-Shaw type). Numerical results confirm the relevance of such limits.

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