COMPLETE BLOW-UP AND GLOBAL BEHAVIOR OF SOLUTIONS OF U(T)-DELTA-U=G(U)

For u(0) epsilon L-infinity(Omega), u(0) greater than or equal to 0, w e study the global behaviour of solutions of the nonlinear heat equati on (1). The domain Omega is smooth and bounded and the nonlinearity g is nonnegrative, nondecreasing and convex. We show in particular that any nondecreasing solution blowing up at the finite time T-max blows u p completely in Omega after T-max. We apply this result to the descrip tion of all possible global behaviours of the solutions of (1) accordi ng to the value of lambda. We show similar results when we introduce a notion of complete blow up in infinite time. (C) Elsevier, Paris.