SEMIDISCRETIZATION IN TIME OF NONLINEAR PARABOLIC EQUATIONS WITH BLOWUP OF THE SOLUTION

In this paper the author considers the first boundary value problem for the nonlinear equation u(t) - Delta u(m) = alpha u(m) in Omega, a smooth bounded domain in R(n) with the zero lateral boundary condition and with a positive initial condition; m is supposed to be larger than one and a positive. A scheme for the discretization in time of that problem is proposed. It is proven that if the exact solution blows up in a finite time, it is the same for the numerical solution. Estimates of the blow-up time are obtained. The stability of the method and the convergence for a class of initial conditions is proved.