$L^1$-Contraction Property of Entropy Solutions for Scalar Conservation Laws with Minimal Regularity Assumptions on the Flux
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912521739304960 |
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| author | Hashash, Paz |
| author_facet | Hashash, Paz |
| contents | This paper is concerned with entropy solutions of scalar conservation laws of the form $\partial_{t}u+\diver f=0$ in $\mathbb{R}^d\times(0,\infty)$. The flux $f=f(x,u)$ depends explicitly on the spatial variable $x$. Using an extension of Kruzkov's method, we establish the $L^1$-contraction property of entropy solutions under minimal regularity assumptions on the flux. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14565 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L^1$-Contraction Property of Entropy Solutions for Scalar Conservation Laws with Minimal Regularity Assumptions on the Flux Hashash, Paz Analysis of PDEs This paper is concerned with entropy solutions of scalar conservation laws of the form $\partial_{t}u+\diver f=0$ in $\mathbb{R}^d\times(0,\infty)$. The flux $f=f(x,u)$ depends explicitly on the spatial variable $x$. Using an extension of Kruzkov's method, we establish the $L^1$-contraction property of entropy solutions under minimal regularity assumptions on the flux. |
| title | $L^1$-Contraction Property of Entropy Solutions for Scalar Conservation Laws with Minimal Regularity Assumptions on the Flux |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.14565 |