方程式u_t=u^δ(Δu+μu)の爆発解の数値解析

抄録

Numerical experiments of the initial boundary value problem for a nonlinear degenerate parabolic equation of nondivergent form are presented in the case of dimension N=2, under zero Dirichlet condition. The emphasis is on a detailed behavior of solutions near the blow-up time. Precise growth rate of solutions is obtained. The numerical results indicate that the blow-up set and the blow-up rate are just those which the theory conjectures.