Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter-Saxton system

被引：8

作者：

Grunert, Katrin ^{[1
]}

Nordli, Anders ^{[1
]}

机构：

[1] Norwegian Univ Sci & Technol, Dept Math Sci, NO-7491 Trondheim, Norway

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2018年 / 15卷 / 03期

关键词：

The two-component Hunter-Saxton system; alpha-dissipative solutions; Lipschitz stability; CAMASSA-HOLM EQUATION; GLOBAL CONSERVATIVE SOLUTIONS;

D O I：

10.1142/S0219891618500182

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the concept of alpha-dissipative solutions for the two-component Hunter-Saxton system under the assumption that either alpha(x) = 1 or 0 <= alpha(x) < 1 for all x is an element of R Furthermore, we investigate the Lipschitz stability of solutions with respect to time by introducing a suitable parametrized family of metrics in Lagrangian coordinates. This is necessary due to the fact that the solution space is not invariant with respect to time.

引用

页码：559 / 597

页数：39

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