Cell-cell adhesion and multiphase Hele-Shaw flow as a singular limit of a Keller-Segel system
ABSTRACT
In this talk, we look at cell-cell adhesion through a large-scale limit of the Patlak-Keller-Segel system. Our primary motivation is the celebrated Differential Adhesion Hypothesis (DAH), a central belief in the study of cell-cell adhesion proposed by Malcolm Steinberg in 1962, which posits that cell populations self-organize by minimizing adhesion energy, in a manner analogous to fluids minimizing surface tension. As the energy governs the evolution and equilibria, we provide an energy converge result. Furthermore, we recover the regimes predicted by the DAH, and lastly, we identify the evolution law of cells as the multiphase Hele-Shaw flow with surface tension.
