Stability and Bifurcations in a Free Boundary PDE Models of Cell Motility

Leonid Berlyand discusses mathematical models for the onset of cell motion driven by myosin contraction. A two-dimensional free-boundary PDE model links cell-shape evolution to diffusion and Keller–Segel-type transport. The talk examines linear stability, a stability-determining eigenvalue and the way nonlinear diffusion changes the bifurcation from supercritical to subcritical. It also considers the curvature of the bifurcation curve, connections to bistability, and the role of non-self-adjoint operators. An example illustrates why a spectral gap alone need not guarantee stability. This is an in-person Analysis of Fluids and Related Topics seminar at Princeton.