A reaction-diffusion system with fast reversible reaction. (Q1413165)

The authors study a diffusion-reaction system of the form \[ \begin{aligned} u_t &= d_1\Delta u-\alpha k(r_A(u)- r_B(v)),\\ v_t &= d_2\Delta v+\beta k(r_A(u)- r_B(v))\end{aligned} \] in a bounded domain with no-flux boundary conditions. Here \(\alpha\), \(\beta\), \(k> 0\). They prove an interesting result concerning the limiting behaviour of \((u,v)\) as \(k\to \infty\).