Existence and Lipschitz stability for α-dissipative solutions of the two-component Hunter–Saxton system
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Original versionJournal of Hyperbolic Differential Equations. 2018, 15 (3), 559-597. 10.1142/S0219891618500182
We establish the concept of α-dissipative solutions for the two-component Hunter–Saxton system under the assumption that either α(x)=1 or 0≤α(x)<1 for all x∈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.