Gradient Catastrophe for Solutions to the Conservation Laws with Source Term
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866913109384364032 |
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| author | Zhao, Qingsong |
| author_facet | Zhao, Qingsong |
| contents | This paper studies singularity formation for conservation laws with a source term. Motivated by John (1974) and Barlin (2023), we prove finite-time blow-up under initial data conditions weaker than those in Barlin. Moreover, we show that a sufficiently small compact support length of the initial data promotes blow-up. Hence, global existence can only be achieved when the initial data have a large compact support length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07487 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gradient Catastrophe for Solutions to the Conservation Laws with Source Term Zhao, Qingsong Analysis of PDEs 35L65, 35B44, 35L67 This paper studies singularity formation for conservation laws with a source term. Motivated by John (1974) and Barlin (2023), we prove finite-time blow-up under initial data conditions weaker than those in Barlin. Moreover, we show that a sufficiently small compact support length of the initial data promotes blow-up. Hence, global existence can only be achieved when the initial data have a large compact support length. |
| title | Gradient Catastrophe for Solutions to the Conservation Laws with Source Term |
| topic | Analysis of PDEs 35L65, 35B44, 35L67 |
| url | https://arxiv.org/abs/2605.07487 |