ON THE BLOW-UP TIME CONVERGENCE OF SEMIDISCRETIZATIONS OF REACTION-DIFFUSION EQUATIONS

Semidiscretizations of reaction-diffusion equations are studied and sp ecial attention is devoted to symmetric solutions. Also nonsymmetric s olutions are considered when the reaction term is such that f(0) = 0. Sufficient conditions for blow-up in such discretizations are establis hed and upper bounds of the blow-up time, which depend on the maximum norm of the initial conditions, are provided, Convergence of the blow- up times of the semidiscrete problems to the theoretical one is proved . (C) 1998 IMACS/Elsevier Science B.V.