Thursday October 9th, 2025 | |
| Time: | 2:15 PM - 3:15 PM |
| Title: | Stability and Bifurcations in a Free Boundary PDE Models of Cell Motility |
| Speaker: | Leonid Berlyand, Penn State |
| Abstract: | |
| We begin with a brief overview of the rapidly developing research area of active matter, a.k.a. active materials. These materials are intrinsically out of equilibrium resulting in novel physical properties whose modeling requires the development of new mathematical tools. We present a free boundary PDE model a cytoskeleton of a moving cell. The key features of our model are the Keller-Segel cross-diffusion term and nonlocal boundary conditions. We first present a recent result on the nonlinear stability of stationary and traveling wave solutions in this model. We discuss novel mathematical features of this free boundary model with a focus on non-self-adjointness, which plays a key role in the spectral stability analysis. We next consider the model above with nonlinear diffusion and prove in a constructive way that such diffusion results in the change of the bifurcation from subcritical to subcritical, which provides physical insights. Finally, we prove the existence of bifurcation from stationary to traveling waves via developing a novel functional setting for the classical Crandall-Rabinowitz theorem. | |