Blow-up analysis for a system of heat equations coupled via nonlinear boundary conditions

In this paper, we study a system of heat equations ut=(delta)u,vt=(delta)v in (omega)*(0,T) coupled via nonlinear boundary conditions (partial)u=epv (partial)u/(partial)n=uq on (partial)(omega)+(0,T)(partial)u/(partial)n=epv,(partial)u (partial)n=uq on ((partial)(omega)*(0,T) Here p, q>0. We prove that the solutions always blow up in finite time for non-trivial and non-negative initial values. We also prove that the blow-up occurs only on SR = (partial)BR for (omega)= BR = {x (epsilon)Rn:|x|