Stable dynamics of spikes in solutions to a system of reaction-diffusion equations (Q2730783)

The authors study the spike dynamics for the following system of reaction-diffusion equations with linear coupling: NEWLINE\[NEWLINE\partial u_1/\partial t= \varepsilon^2\Delta u_1+ F(u_1)+ \sigma(u_1- u_2),NEWLINE\]NEWLINE NEWLINE\[NEWLINE\tau\partial u_2/\partial t= \varepsilon^2\Delta u_2+ F(u_1)+ \sigma(u_1- u_2)\quad \text{in }\Omega,NEWLINE\]NEWLINE NEWLINE\[NEWLINE\partial u_1/\partial n= \partial u_2/\partial n= 0\quad \text{on }\partial\Omega,NEWLINE\]NEWLINE where \(0< \varepsilon< 1\), \(\sigma>0\) and \(0<\tau<1\) are constants, and \(\Omega\subset \mathbb{R}^3\) is a smooth bounded domain, \(n\) is the outward unit normal to \(\partial\Omega\), \(F(s)= s^2- s\).