Lipschitz Stability for the Hunter-Saxton Equation

Katrin Grunert; Matthew Tandy

doi:10.1142/S0219891622500072

Lipschitz Stability for the Hunter-Saxton Equation

Analysis of PDEs 2022-10-20 v3

Authors: Katrin Grunert , Matthew Tandy

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Abstract

We study the Lipschitz stability in time for $\alpha$ -dissipative solutions to the Hunter-Saxton equation, where $\alpha \in [0,1]$ is a constant. We define metrics in both Lagrangian and Eulerian coordinates, and establish Lipschitz stability for those metrics.

Keywords

stability analysis stability theory

Cite

@article{arxiv.2103.10227,
  title  = {Lipschitz Stability for the Hunter-Saxton Equation},
  author = {Katrin Grunert and Matthew Tandy},
  journal= {arXiv preprint arXiv:2103.10227},
  year   = {2022}
}

Comments

Third Version: Corrected some typos and small mistakes noticed after submission. Added a missing condition in the definition of the set of Eulerian coordinates

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