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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.19313 |
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| _version_ | 1866908419017932800 |
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| author | Yin, Huicheng Zhu, Wanqing |
| author_facet | Yin, Huicheng Zhu, Wanqing |
| contents | In the paper [Li Jun, Xu Gang, Yin Huicheng, On the blowup mechanism of smooth solutions to 1D quasilinear strictly hyperbolic systems with large variational initial data, Nonlinearity 38 (2025), No.2, 025016], for the 1-D $n\times n$ ($n\geqslant 3$) strictly hyperbolic system $\partial_tv+F(v)\partial_xv=0$ with some classes of large variational initial data $v(x, 0)$, the geometric blowup mechanism and the detailed singularity behaviours of $\partial_{x,t}v$ near the blowup point are studied when the $n\times n$ matrix $F(v)$ admits at least one genuinely nonlinear eigenvalue. In this paper, we focus on the formation and construction of a large variational shock wave from the blowup point for 1-D $n\times n$ quasilinear hyperbolic conservation law system $\partial_tu+\partial_xf(u)=0$ when some smooth simple wave solution is generic non-degenerate before the formation of singularity and the corresponding eigenvalue is genuinely nonlinear. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19313 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formation and construction of large variational shock waves for 1-D $n\times n$ quasilinear hyperbolic conservation systems Yin, Huicheng Zhu, Wanqing Analysis of PDEs In the paper [Li Jun, Xu Gang, Yin Huicheng, On the blowup mechanism of smooth solutions to 1D quasilinear strictly hyperbolic systems with large variational initial data, Nonlinearity 38 (2025), No.2, 025016], for the 1-D $n\times n$ ($n\geqslant 3$) strictly hyperbolic system $\partial_tv+F(v)\partial_xv=0$ with some classes of large variational initial data $v(x, 0)$, the geometric blowup mechanism and the detailed singularity behaviours of $\partial_{x,t}v$ near the blowup point are studied when the $n\times n$ matrix $F(v)$ admits at least one genuinely nonlinear eigenvalue. In this paper, we focus on the formation and construction of a large variational shock wave from the blowup point for 1-D $n\times n$ quasilinear hyperbolic conservation law system $\partial_tu+\partial_xf(u)=0$ when some smooth simple wave solution is generic non-degenerate before the formation of singularity and the corresponding eigenvalue is genuinely nonlinear. |
| title | Formation and construction of large variational shock waves for 1-D $n\times n$ quasilinear hyperbolic conservation systems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.19313 |