Existence of BV solutions for $2\times2$ hyperbolic balance laws for $L^\infty$ initial data
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909277401120768 |
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| author | Haspot, Boris Jana, Animesh |
| author_facet | Haspot, Boris Jana, Animesh |
| contents | We prove the existence of BV solutions for $2\times 2$ system of hyperbolic balance laws in one space dimension. The flux is assumed to have two genuinely nonlinear characteristic fields. We consider a general force which may possibly depend on time and space variable as well. To prove the existence, we assume the initial data to be small in $L^\infty$. Furthermore, we also study qualitative behavior for entropy solutions to hyperbolic system of balance laws. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00849 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of BV solutions for $2\times2$ hyperbolic balance laws for $L^\infty$ initial data Haspot, Boris Jana, Animesh Analysis of PDEs We prove the existence of BV solutions for $2\times 2$ system of hyperbolic balance laws in one space dimension. The flux is assumed to have two genuinely nonlinear characteristic fields. We consider a general force which may possibly depend on time and space variable as well. To prove the existence, we assume the initial data to be small in $L^\infty$. Furthermore, we also study qualitative behavior for entropy solutions to hyperbolic system of balance laws. |
| title | Existence of BV solutions for $2\times2$ hyperbolic balance laws for $L^\infty$ initial data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.00849 |