Free Boundary Problems 2026

Incompressible limit and pressure jump in the Cahn-Hilliard equation

9 Sept 2026, 14:00

30m

Main Building/Floor 1-Room 2091 - Lecture Hall (HU (Main Building))

Phase Transitions and Pattern Formation Phase Transitions and Pattern Formation

Speaker

Charles Elbar (Université Claude Bernard Lyon 1)

Description

We consider a simplified model for tumor growth: a Cahn-Hillard equation with a repulsive potential, that models the pressure inside the tissue. This potential is of the form u^{\gamma}. In the so-called incompressible limit when gamma is sent to infinity, we observe that the pressure admits a jump at the free boundary of the model. This is a joint work with Benoît Perthame and Jakub Skrzeczkowski.