Special Session 173: Mathematical and Numerical Analysis on Nonlinear PDEs

Analytical and numerical results on the global bifurcation structure of a cell polarization problem
Tatsuki Mori
Musashino University
Japan
Co-Author(s):    Tatsuki Mori
Abstract:
We investigate the global bifurcation structure of solutions for a nonlinear boundary value problem with a nonlocal constraint arising in a cell polarization model with mass conservation proposed by Mori, Jilkine, and Edelstein-Keshet. Regarding the shadow system of the stationary problem, a representation formula for the solutions and the global bifurcation diagrams have already been obtained. In this talk, we derive a representation formula for the solutions of the original problem and report on numerical simulations of its global bifurcation diagram. In particular, global bifurcation diagrams include secondary and imperfect bifurcation phenomena.