FINITE DIFFERENCE METHOD OF FIRST BOUNDARY PROBLEM FOR QUASILINEAR PARABOLIC SYSTEMS(Continued)

摘要

In this paper, we consider the existence, uniqueness and convergence of weak and strongimplicit difference solution for the first boundary problem of quasilinear parabolic system: u_t=（-1）M+1A(x,t,u,…,u_xM-1)u_x2M+f(x,t,u,…,u_x2M-1), （x,t）∈Q_T={0xl, 0t≤T}, （1） u_xk（0,t）=u_xk（l,t）=0,（k=0,1,…,M-1）, 0t≤T, （2） u（x,0） =ψ（x）, 0≤x≤l, （3）where u, ψ and f are m-dimensional vector valued functions, A is an m×m positivelydefinite matrix and u_xk denotes ?ku/?_xk. For this problem, the estimations of the differencesolution are obtained. As h→0, △t→0, the difference solution converges weakly in W₂2M,1 （QT）to the unique generalized solution u（x,t）∈W₂2M,1（QT） of problems （1）, （2）, （3）. Especially,a favorable restriction condition to the step lengths △t and h for explicit and weak implicitschemes is found.