Existence and Lipschitz stability for $\alpha$-dissipative solutions of the two-component Hunter-Saxton system

Katrin Grunert, Anders Nordli

We establish the concept of $\alpha$-dissipative solutions for the two-component Hunter-Saxton system under the assumption that either $\alpha (x)=1$ or $0\le \alpha (x)<1$ for all $x\in \mathbb{R…