On equivalence of entropy and viscosity solutions to degenerate parabolic equations and applications
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913843121225728 |
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| author | Mitake, Hiroyoshi Watanabe, Hiroshi |
| author_facet | Mitake, Hiroyoshi Watanabe, Hiroshi |
| contents | Here, we consider anisotropic degenerate parabolic-hyperbolic equations and degenerate quasilinear Hamilton-Jacobi equations. We prove the equivalence of two notions of entropy and viscosity solutions of two equations, and apply it to obtain a large-time behavior of viscosity solutions to quasilinear Hamilton-Jacobi equations, and entropy solutions to degenerate parabolic-hyperbolic equations in a periodic setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04960 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On equivalence of entropy and viscosity solutions to degenerate parabolic equations and applications Mitake, Hiroyoshi Watanabe, Hiroshi Analysis of PDEs 35K65, 35D30, 49L25 Here, we consider anisotropic degenerate parabolic-hyperbolic equations and degenerate quasilinear Hamilton-Jacobi equations. We prove the equivalence of two notions of entropy and viscosity solutions of two equations, and apply it to obtain a large-time behavior of viscosity solutions to quasilinear Hamilton-Jacobi equations, and entropy solutions to degenerate parabolic-hyperbolic equations in a periodic setting. |
| title | On equivalence of entropy and viscosity solutions to degenerate parabolic equations and applications |
| topic | Analysis of PDEs 35K65, 35D30, 49L25 |
| url | https://arxiv.org/abs/2408.04960 |