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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.11689 |
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| _version_ | 1866913844283047936 |
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| author | Cheng, Jeffrey |
| author_facet | Cheng, Jeffrey |
| contents | We study extremal shocks of $1$-d hyperbolic systems of conservation laws which fail to be genuinely nonlinear. More specifically, we consider either $1$- or $n$-shocks in characteristic fields which are either concave-convex or convex-concave in the sense of LeFloch. We show that the theory of $a$-contraction can be applied to obtain $L^2$-stability up to shift for these shocks in a class of weak solutions to the conservation law whose shocks obey the Lax entropy condition. Our results apply in particular to the $2 \times 2$ system of nonlinear elastodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relative Entropy Contractions for Extremal Shocks of Nonlinear Hyperbolic Systems without Genuine Nonlinearity Cheng, Jeffrey Analysis of PDEs We study extremal shocks of $1$-d hyperbolic systems of conservation laws which fail to be genuinely nonlinear. More specifically, we consider either $1$- or $n$-shocks in characteristic fields which are either concave-convex or convex-concave in the sense of LeFloch. We show that the theory of $a$-contraction can be applied to obtain $L^2$-stability up to shift for these shocks in a class of weak solutions to the conservation law whose shocks obey the Lax entropy condition. Our results apply in particular to the $2 \times 2$ system of nonlinear elastodynamics. |
| title | Relative Entropy Contractions for Extremal Shocks of Nonlinear Hyperbolic Systems without Genuine Nonlinearity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.11689 |