TY - JOUR
T1 - A Hopf Bifurcation in a Generalized Mckean Type of Free Boundary Problem Satisfying the Dirichlet Boundary Condition
JO - Journal of Partial Differential Equations
VL - 1
SP - 71
EP - 84
PY - 1999
DA - 1999/12
SN - 12
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5526.html
KW - Evolution equation
KW - free boundary problem
KW - Hopf bifurcation
KW - internal layer solution
KW - parabolic equation
AB -  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.