2 papers
math.AP2025
Change of bifurcation type in 2D free boundary model of a moving cell with nonlinear diffusion
Leonid Berlyand, Oleksii Krupchytskyi, Tim Laux
We introduce a 2D free boundary problem with nonlinear diffusion that models a living cell moving on a substrate. We prove that this nonlinearity results in a qualitative of soluti…
math.AP2024
Nonlinear stability in a free boundary model of active locomotion
Leonid Berlyand, C. Alex Safsten, Lev Truskinovsky
Contraction-driven self-propulsion of a large class of living cells can be modeled by a Keller-Segel system with free boundaries. The ensuing "active" system, exhibiting both dissi…