I tiakina i:
| Ngā kaituhi matua: | , , , |
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| Hōputu: | Preprint |
| I whakaputaina: |
2022
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| Ngā marau: | |
| Urunga tuihono: | https://arxiv.org/abs/2204.02421 |
| Ngā Tūtohu: |
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| _version_ | 1866917603950198784 |
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| author | Bressan, Alberto Galtung, Sondre T. Grunert, Katrin Nguyen, Khai T. |
| author_facet | Bressan, Alberto Galtung, Sondre T. Grunert, Katrin Nguyen, Khai T. |
| contents | This paper provides an asymptotic description of a solution to the Burgers-Hilbert equation in a neighborhood of a point where two shocks interact. The solution is obtained as the sum of a function with $H^2$ regularity away from the shocks plus a corrector term having an asymptotic behavior like |x|ln|x| close to each shock. A key step in the analysis is the construction of piecewise smooth solutions with a single shock for a general class of initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_02421 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Shock interactions for the Burgers-Hilbert Equation Bressan, Alberto Galtung, Sondre T. Grunert, Katrin Nguyen, Khai T. Analysis of PDEs 35L65, 35L60, 35L03 This paper provides an asymptotic description of a solution to the Burgers-Hilbert equation in a neighborhood of a point where two shocks interact. The solution is obtained as the sum of a function with $H^2$ regularity away from the shocks plus a corrector term having an asymptotic behavior like |x|ln|x| close to each shock. A key step in the analysis is the construction of piecewise smooth solutions with a single shock for a general class of initial data. |
| title | Shock interactions for the Burgers-Hilbert Equation |
| topic | Analysis of PDEs 35L65, 35L60, 35L03 |
| url | https://arxiv.org/abs/2204.02421 |