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

Abstract:

      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）．