A Lipschitz metric for $α$-dissipative solutions to the Hunter-Saxton equation (2302.07150v2)

Abstract: 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 $-dissipative solutions constructed using a generalised method of characteristics approach, where $\alpha$ is a function determining the energy loss at each position in space.