A Lipschitz metric for \(\alpha \)-dissipative solutions to the Hunter–Saxton equation

We explore the Lipschitz stability of solutions to the Hunter–Saxton equation with respect to the initial data. In particular, we study the stability of \( \alpha \) $\alpha$ -dissipative solutions constructed using a generalised method of characteristics approach, where \(\alpha \) $\alpha$ is a function determining the energy loss at each position in space.