知识与财富的链接
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 ｕｔ＋λ（ｕ）ｕx＝０,ｕ｜Γ＝φ（ｘ）,Γ：ｘ＝x（σ）,ｔ＝t（σ）．