Abstract
We establish the concept of [Formula: see text]-dissipative solutions for the two-component Hunter–Saxton system under the assumption that either [Formula: see text] or [Formula: see text] for all [Formula: see text]. 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.
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