对角型拟线性双曲系统在大初值下整体光滑解的存在性

EXISTENCE OF GLOBALLY SMOOTH SOLUTIONS IN DIAGONAL FORM OF QUASILINEAR HYPERBOLIC SYSTEMS UNDER LARGE INITIAL DATA

Hoff证明了在A和初值u_0(x)的某些光滑性、单调性的条件下有整体光滑解存在。在(1),(2)中,u∈R^n,Λ(x,t,u)=diag(λ~1,…,λ~n)为对角n×n矩阵,它具有双曲性:当i≠j、(x,t,u)∈R×R_(≥0)×R^n时,λ~i(x,t,u)≠λ~i(x,t,u)。

In this paper,we have improved the Hoff's results and proved the existence of globally smooth solutions of system (1),(2) under large initial data by using a new,simple method.