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Existence And Lipschitz Stability For α-dissipative Solutions Of The Two-component Hunter–Saxton System

Katrin Grunert, Anders Nordli

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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.