Abstract: For the strictly monotonic schemes approximating single hyperbolic conservation laws, the asymptotic stability of the discrete shocks is widely believed to have been worked out. But in fact, in all of the former works, both in results and in proofs, some mistakes occurred. In the present paper, we expose the correct result and give a rigorous proof.

Key words: hyperbolic conservation law, discrete shock, asymptotic stability

摘要： 多年以来，近似双曲型守恒律方程的严格单调差分格式的离散激波的渐近稳定性一直被普遍认为已经得到解决。但事实上前人的工作中，不论是结论的叙述，还是证明，都或多或少地存在一些错误。本文给出了这一结果的正确叙述和严格证明，从而澄清了多年来的错误认识。

关键词: 双曲型守恒律, 离散激波, 渐近稳定性