森 竜樹

This paper studies the Neumann problem of a nonlocal Allen-Cahn equation in an interval. A main result finds a symmetry breaking (secondary) bifurcation point on the bifurcation curve of solutions with odd-symmetry. Our proof is based on a level set analysis for the associated integral map. A method using the complete elliptic integrals proves the uniqueness of secondary bifurcation point. We also show some numerical simulations concerning the global bifurcation structure. (C) 2017 Elsevier Inc. All rights reserved.

We show existence, nonexistence, and exact multiplicity for stationary limiting problems of a cell polarization model proposed by Y. Mori, A. Jilkine and L. Edelstein-Keshet. It is a nonlinear boundary value problem with total mass constraint. We obtain exact multiplicity results by investigating a global bifurcation sheet which we constructed by using complete elliptic integrals in a previous paper.