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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.04640 |
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| _version_ | 1866929745377099776 |
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| author | Haspot, Boris Jana, Animesh |
| author_facet | Haspot, Boris Jana, Animesh |
| contents | We study the vanishing viscosity limit for $2\times2$ triangular system of hyperbolic conservation laws when the viscosity coefficients are non linear. In this article, we assume that the viscosity matrix $B(u)$ is commutating with the convective part $A(u)$. We show the existence of global smooth solution to the parabolic equation satisfying uniform total variation bound in $\varepsilon$ provided that the initial data is small in $BV$. This extends the previous result of Bianchini and Bressan [Commun. Pure Appl. Anal. (2002)] which was considering the case $B(u)=I$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Viscous approximation of triangular system in 1-d with nonlinear viscosity Haspot, Boris Jana, Animesh Analysis of PDEs We study the vanishing viscosity limit for $2\times2$ triangular system of hyperbolic conservation laws when the viscosity coefficients are non linear. In this article, we assume that the viscosity matrix $B(u)$ is commutating with the convective part $A(u)$. We show the existence of global smooth solution to the parabolic equation satisfying uniform total variation bound in $\varepsilon$ provided that the initial data is small in $BV$. This extends the previous result of Bianchini and Bressan [Commun. Pure Appl. Anal. (2002)] which was considering the case $B(u)=I$. |
| title | Viscous approximation of triangular system in 1-d with nonlinear viscosity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.04640 |