An informal account of recent results on initial-boundary value problems for systems of conservation laws
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917656374804480 |
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| author | Spinolo, Laura V. Ancona, Fabio Marson, Andrea |
| author_facet | Spinolo, Laura V. Ancona, Fabio Marson, Andrea |
| contents | This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [4]. In that paper, the authors established new global-in-time existence results for admissible solutions of nonlinear systems of conservation laws defined in domains with boundaries. The main novelty in [4] is that the solution is constructed by taking into account the underlying viscous mechanism, which is relevant because, in the case of initial-boundary value problems, different viscous approximations yield in general different limits. This note will frame the analysis of [4] in the relevant context, compare the main result with the previous existing literature, and touch upon the most innnovative technical points of the proof. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An informal account of recent results on initial-boundary value problems for systems of conservation laws Spinolo, Laura V. Ancona, Fabio Marson, Andrea Analysis of PDEs 35L65, 35B30 This note aims at providing a rather informal and hopefully accessible overview of the fairly long and technical work [4]. In that paper, the authors established new global-in-time existence results for admissible solutions of nonlinear systems of conservation laws defined in domains with boundaries. The main novelty in [4] is that the solution is constructed by taking into account the underlying viscous mechanism, which is relevant because, in the case of initial-boundary value problems, different viscous approximations yield in general different limits. This note will frame the analysis of [4] in the relevant context, compare the main result with the previous existing literature, and touch upon the most innnovative technical points of the proof. |
| title | An informal account of recent results on initial-boundary value problems for systems of conservation laws |
| topic | Analysis of PDEs 35L65, 35B30 |
| url | https://arxiv.org/abs/2405.02096 |