TY - JOUR
T1 - Global Coupling of an Interface Problem in an Activator-inhibitor System
AU - YoonMee Ham 
JO - Journal of Partial Differential Equations
VL - 2
SP - 135
EP - 147
PY - 2003
DA - 2003/05
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5412.html
KW - activator-inhibitor
KW - van der Pol equation
KW - global coupling
KW - free boundary problem
KW - Hopf bifurcation
AB -  An activator-inhibitor reaction system with global coupling was introduced in [1]. The authors showed that global coupling suppresses the breathing motion and enhances the propagation of the localized solution. The collision between two traveling waves for a sufficiently strong global coupling is discussed in [2]. If the width of layers is infinitesimally thin, the equation of motion for a pair of the interfaces is derived. We shall study the dynamics of interfaces in the free boundary problem with global coupling and with a strong global coupling.