The ability of crawling cells to exhibit persistent, steady motion is crucial to various biological processes, ranging from wound healing to the immune response. Interestingly, even small changes of either biological or physical mechanisms driving cell motion may have drastic effects on their behavior, such as loss of motion or non-straight line motility. We use both analysis and numerical simulations to study a partial differential equation model of cell motility. Since traveling wave solutions correspond to persistent cell motion, their existence and stability is a central question: we establish existence of traveling waves, and numerically study the stability of their motion.

This is joint work completed with L. Berlyand during my PhD, together with V. Rybalko, L. Zhang, and P. Zhang.