Asymptotic Behavior of Global Classical Solutions of Quasilinear Non-strictly Hyperbolic Systems with Weakly Linear Degeneracy

在这篇论文，我们学习一般的伪的 Cauchy 问题的全球古典解决方案的 asymptotic 行为有多重的常数并且弱的线性夸张系统线性地堕落典型领域。基于周毅等证明的全球古典答案的存在，我们证明当 t 趋于到无穷时，答案接近 C^1 旅行波浪答案的联合，如果全部的变化和起始的数据的 L^1 标准是足够地小的。

In this paper, we study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with constant multiple and weakly linearly degenerate characteristic fields. Based on the existence of global classical solution proved by Zhou Yi et al., we show that, when t tends to infinity, the solution approaches a combination of C^1 travelling wave solutions, provided that the total variation and the L^1 norm of initial data are sufficiently small.