BLOW-UP OF SOLUTIONS OF NONLINEAR PARABOLIC EQUATIONS

In chapter 1 we prove that for the parabolic initial value prob- lem u(,t) = (DELTA)u + (delta)f(u) there is a finite time blow-up of the solution, provided (delta) is greater than the upper bound to the spectrum of the steady rate problem and (f/f\u27) is concave. An upper bound of the blow-up time is given. The proof is based on a comparison with a supersolution to the parabolic initial value problem. In chapter 2 we study the blow-up set of solutions of the equation (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) For the radially symmetric case we prove that the blow-up set consist of a single point. In the general case we prove that the blow-up set is a compact subset of (OMEGA). Estimates of the rate of blow-up are given