# A Hele-Shaw tumor growth model as a gradient flow. – Simone Di Marino (Scuola Normale Superiore)

#### Venue

Sala Seminari (Dip. Matematica).

#### 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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