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

被引：7
|
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
收藏
页码：559 / 597
页数：39
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