A Lipschitz metric for $α$-dissipative solutions to the Hunter-Saxton equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910499141058560 |
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| author | Grunert, Katrin Tandy, Matthew |
| author_facet | Grunert, Katrin Tandy, Matthew |
| contents | 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 $ α$-dissipative solutions constructed using a generalised method of characteristics approach, where $α$ is a function determining the energy loss at each position in space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07150 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Lipschitz metric for $α$-dissipative solutions to the Hunter-Saxton equation Grunert, Katrin Tandy, Matthew Analysis of PDEs Primary: 35B35, 37L15, Secondary: 35Q35, 35L67 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 $ α$-dissipative solutions constructed using a generalised method of characteristics approach, where $α$ is a function determining the energy loss at each position in space. |
| title | A Lipschitz metric for $α$-dissipative solutions to the Hunter-Saxton equation |
| topic | Analysis of PDEs Primary: 35B35, 37L15, Secondary: 35Q35, 35L67 |
| url | https://arxiv.org/abs/2302.07150 |