Formation of singularities in solutions to nonlinear hyperbolic systems with general sources
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909454610464768 |
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| author | Bärlin, Johannes |
| author_facet | Bärlin, Johannes |
| contents | We consider nonlinear hyperbolic systems with a general source and prove that for appropriately chosen smooth initial data the lifespan of the associated $C^1$-solution $u$ cannot be infinite. We employ ideas of F. John (1974) and L. Hörmander (1987) to show that the derivative $u_x$ of $u$ becomes unbounded in finite time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_12101 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Formation of singularities in solutions to nonlinear hyperbolic systems with general sources Bärlin, Johannes Analysis of PDEs We consider nonlinear hyperbolic systems with a general source and prove that for appropriately chosen smooth initial data the lifespan of the associated $C^1$-solution $u$ cannot be infinite. We employ ideas of F. John (1974) and L. Hörmander (1987) to show that the derivative $u_x$ of $u$ becomes unbounded in finite time. |
| title | Formation of singularities in solutions to nonlinear hyperbolic systems with general sources |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2204.12101 |