“双曲抛物偏微分方程奇异摄动问题的差分解法”的一个注记

A NOTE ON "A DIFFERENCE METHOD FOR SINGULAR PERTURBATION PROBLEM OF HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATION

本文对下述边值问题εＵ＿（ｔｔ）＋Ｕ＿ｔ－Ｕ＿（ｘｘ）＝ｆ（ｘ，ｔ） ０＜Ｘ＜１，０＜ｔ＜ＴＵ（０，ｔ）＝Ｕ（１，ｔ）＝０ ０＜ｔ＜ＴＵ（ｘ，０）＝Ｓ（ｘ），Ｕｔ（ｘ，０）＝Ｗ（ｘ） ０＜ｘ＜１的可解性进行了研究，认为可以放宽文［１］中对函数ｆ、ｓ、ｗ所作的假定，满足一般的可积性条件即可．

In this paper,we consider the solvable condition of the boundary value problem:εUtt+Ut-Uxx=f(x,t) 0<x<1 , 0<t<TU(0,t) =U(1,t) =0 0<t<TU(x, 0)=S(x), Ut(x, 0)=w (x) 0<x<1 We hold that the suppositions on the functions f,s, win the article [1] could be soften the terms, it is enough for the functions f,s, w if letthem to sans fy general integrability condition.