两类拟线性波型方程的结构稳定尖点奇异性的正则性

中文摘要 AI 辅助

本文研究了两族拟线性方程：Hunter-Saxton型和Camassa-Hom型方程，其中参数λ∈(0,1)使得解形成尖点奇异性。当λ=1时，第一个系统退化为标量守恒律。本文的主要结果是给出两类结构稳定奇异性的正则性：I型在奇异曲线上，II型在尖点奇异性形成的点处，对于某些λ∈(0,1)。当λ→1时，我们的结果表明在奇异性形成点处具有C^{1/3}正则性，这与一般预激波解的正则性一致。

英文摘要

In this paper, we study two families of quasilinear equations: Hunter-Saxton type and Camassa-Hom type equations, with a paramerter $λ\in(0,1)$ whose solutions form cusp singularities. When $λ=1$, the first system becomes the scalar conservation law. The main result of this paper is to give regularity of two types of structurally stable singularities: Type I on the singular curve, Type II at the point where cusp singularity forms, for some $λ\in(0,1)$. When $λ\rightarrow 1$, our result indicts the $C^{1/3}$ regularity at the point where singularity forms, which agrees with the regularity of the generic pre-shock solution.

发表机构

• University of Kansas（堪萨斯大学）
• Wayne State University（韦恩州立大学）

机构由 AI 辅助整理，请以论文原文为准。