一阶拟线性偏微分方程广义Cauchy问题的整体光滑解

On the Global Smooth Solution for Generalized Cauchy Problem of First Order Quasilinear P.D.E.

本文研究了下列一阶拟线性偏微分方程的广义Ｃａｕｃｈｙ问题：ｕｔ＋λ（ｕ）ｕｘ＝０，ｕ｜Γ＝φ（ｘ），Γ：ｘ＝ｒ（σ），ｔ＝ｓ（σ）．证明了该问题在一定条件下，于上半平面Ω＝｛－∞＜ｘ＜＋∞，ｔ≥０｝上存在整体光滑解．

We proper the existence of global smooth solution on Ω={-∞,<x<+∞,t≥0} for the generralized Cauchy problem of first order quasilinear P.D.E which is u t+λ(u)u x=0,u| Γ=φ(x),Γ:x=x(σ),t=t(σ) .