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

Published 14 Feb 2023 in math.AP | (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.

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