On a Hamiltonian regularization of scalar conservation laws
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929267532627968 |
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| author | Guelmame, Billel |
| author_facet | Guelmame, Billel |
| contents | In this paper, we propose a Hamiltonian regularization of scalar conservation laws, which is parametrized by $\ell > 0$ and conserves an $H^1$ energy. We prove the existence of global weak solutions for this regularization. Furthermore, we demonstrate that as $\ell$ approaches zero, the unique entropy solution of the original scalar conservation law is recovered, providing justification for the regularization. This regularization belongs to a family of non-diffusive, non-dispersive regularizations that were initially developed for the shallow-water system and extended later to the Euler system. This paper represents a validation of this family of regularizations in the scalar case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_02218 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Hamiltonian regularization of scalar conservation laws Guelmame, Billel Analysis of PDEs In this paper, we propose a Hamiltonian regularization of scalar conservation laws, which is parametrized by $\ell > 0$ and conserves an $H^1$ energy. We prove the existence of global weak solutions for this regularization. Furthermore, we demonstrate that as $\ell$ approaches zero, the unique entropy solution of the original scalar conservation law is recovered, providing justification for the regularization. This regularization belongs to a family of non-diffusive, non-dispersive regularizations that were initially developed for the shallow-water system and extended later to the Euler system. This paper represents a validation of this family of regularizations in the scalar case. |
| title | On a Hamiltonian regularization of scalar conservation laws |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.02218 |