# A Hele-Shaw tumor growth model as a gradient flow

## Simone Di Marino (Scuola Normale Superiore)

created by gelli on 29 Oct 2017

8 nov 2017 -- 17:00   [open in google calendar]

Sala Seminari Dipartimento di matematica di Pisa

Abstract.

In 2014 Perthame, Quiroz and Vasquez unite two types of modeling of tumor growth into a unique framework of reaction-diffusion type where the diffusive term is $\Delta p(\rho)$ and $p(\rho)=\rho^m$. The stiff limit $m \to \infty$ is in particular a Hele-Shaw type problem: we find a gradient flow formulation of this problem, namely it is the gradient flow of the negative mass with respect to the Wasserstein-Fisher-Rao distance, discovered simultaneously by many authors in the last years. This leads also to accurate numerical simulations of the stiff limit case

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