2 x 2 hyperbolic systems of conservation laws in classes of functions of bounded p-variation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914783187435520 |
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| author | Glass, Olivier |
| author_facet | Glass, Olivier |
| contents | In this paper, we consider $2 \times 2$ hyperbolic systems of conservation laws in one space dimension with characteristic fields satisfying a condition that encompasses genuine nonlinearity and linear degeneracy as well as intermediate cases, namely, with standard notations, $r_i\cdot \nabla λ_i \geq 0$.
We prove the existence of entropy solutions in the fractional $BV$ spaces ${W}_p(\mathbb{R})$ of functions of bounded $p$-variation, $p \in [1,\frac{3}{2}]$, for small initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02123 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 2 x 2 hyperbolic systems of conservation laws in classes of functions of bounded p-variation Glass, Olivier Analysis of PDEs 35L60, 26A45, 35D30 In this paper, we consider $2 \times 2$ hyperbolic systems of conservation laws in one space dimension with characteristic fields satisfying a condition that encompasses genuine nonlinearity and linear degeneracy as well as intermediate cases, namely, with standard notations, $r_i\cdot \nabla λ_i \geq 0$. We prove the existence of entropy solutions in the fractional $BV$ spaces ${W}_p(\mathbb{R})$ of functions of bounded $p$-variation, $p \in [1,\frac{3}{2}]$, for small initial data. |
| title | 2 x 2 hyperbolic systems of conservation laws in classes of functions of bounded p-variation |
| topic | Analysis of PDEs 35L60, 26A45, 35D30 |
| url | https://arxiv.org/abs/2405.02123 |