Shock formation in 1D conservation laws I: Inviscid structure
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911015804862464 |
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| author | Anderson, John Chaturvedi, Sanchit Graham, Cole |
| author_facet | Anderson, John Chaturvedi, Sanchit Graham, Cole |
| contents | We study the stability and structure of shock formation in 1D hyperbolic conservation laws. We show that shock formation is stable near shocking simple waves: perturbations form a shock nearby in spacetime. We also characterize the boundary of the classical development in a spacetime neighborhood of the first time singularity. Finally, we describe the precise nature of nondegenerate shock formation through an expansion in homogeneous functions of fractional degree. We use these results in a companion paper to study the vanishing viscosity limit near shock formation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_17148 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shock formation in 1D conservation laws I: Inviscid structure Anderson, John Chaturvedi, Sanchit Graham, Cole Analysis of PDEs 35L67, 35L65, 76N30 We study the stability and structure of shock formation in 1D hyperbolic conservation laws. We show that shock formation is stable near shocking simple waves: perturbations form a shock nearby in spacetime. We also characterize the boundary of the classical development in a spacetime neighborhood of the first time singularity. Finally, we describe the precise nature of nondegenerate shock formation through an expansion in homogeneous functions of fractional degree. We use these results in a companion paper to study the vanishing viscosity limit near shock formation. |
| title | Shock formation in 1D conservation laws I: Inviscid structure |
| topic | Analysis of PDEs 35L67, 35L65, 76N30 |
| url | https://arxiv.org/abs/2506.17148 |