Exposé de Charles ELBAR

Pressure jump in the Cahn-Hilliard equation

Abstract: We are interested in quantifying the pressure jump at the interface of a tumor, assmuming it is an incompressible flow. This jump is related to two antagonistic effects: repulsion of cells when the tumor grows and cell-cell adhesion which creates surface tension. To take into account these two effects, we use the Cahn-Hilliard equation. To compute this pressure jump, we also include an external force and consider stationary radial solutions of the Cahn-Hilliard equation. We also characterize completely the stationary solutions in the incompressible case, prove the incompressible limit and prove convergence of the parabolic problems to stationary states.