The blow-up rate for a strongly coupled system of semilinear heat equations with nonlinear boundary conditions

The paper deals with the blow-up rate of positive solutions to the system u (t) = u(xx) + u(l11)v(l12), v(t) = v(xx) + u(l21)v(l22) with boundary condi tions u(x)(1, t) = (u(P11)v(P12))(1,t) and v(x)(1, t) = (u(P21)v(P22))(1, t ). Under some assumptions on the matrices L = (l(ij)) and P = (p(ij)) and o n the initial data u(0), v(0), the solution (u, v) lows up at finite time T , and we prove that max(x epsilon [0,1]) u(x,t) (resp. max x (epsilon [0,1] ) v(x,t)) goes to infinity as (T - t)(alpha1/2) (resp. (T- t)(alpha2/2)), w here alpha (i) < 0 are the solutions of (P - Id)(<alpha>(1,) alpha (2))(t) = (-1, - 1)(t). (C) 2001 Academic Press.