I am a PhD student in Applied Mathematics at Laboratoire Jacques-Louis Lions. I am working under the supervision of Benoît Perthame (LJLL) and Emmanuel Grenier (UMPA, ENS Lyon). My research interests are Partial Differential Equations and their application to living tissue and cancer modelling, mainly with Cahn-Hilliard equation and Hele-Shaw models.
PhD in Applied Mathematics, 2021-present
Sorbonne Université, Paris, France
The Cahn-Hilliard equation with degenerate mobility is used in several areas including the modeling of living tissues. We compute the pressure jump in the small dispersion regime. We also characterize compactly supported stationary solutions in the incompressible case, prove the incompressible limit and prove convergence of the parabolic problems to stationary states.
The Keller-Segel model is a well-known system representing chemotaxis in living organisms. We study the convergence of a generalized nonlinear variant of the Keller-Segel to the degenerate Cahn-Hilliard system and its incompressible limit.