A Lipschitz metric for $\alpha$-dissipative solutions to the Hunter-Saxton equation

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.

arXiv comment43 pages

References in corpus (4)

• Lipschitz metric for the periodic Camassa-Holm equation
• A Lipschitz metric for the Hunter-Saxton equation
• Existence and Lipschitz stability for $\alpha$-dissipative solutions of the two-component Hunter-Saxton system
• Lipschitz Stability for the Hunter-Saxton Equation

Cited by in corpus (2)

• A numerical view on α-dissipative solutions of the Hunter-Saxton equation
• Rate of convergence for numerical $\alpha$-dissipative solutions of the Hunter-Saxton equation