A Hopf Bifurcation in a Generalized Mckean Type of Free Boundary Problem Satisfying the Dirichlet Boundary Condition

Abstract

In this paper, we consider the free boundary problem satisfying the Dirichlet boundary condition. This problem is derived from the reaction diffusion equations with the generalized McKean reaction dynamics. We shall show a Hopf bifurcation occurs at some critical point τ when the stationary solution (v^⋅ (x), s^⋅) satisfies 1/3 < s^⋅ < 1.