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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.15603 |
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| _version_ | 1866911370399711232 |
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| author | Imagawa, Masaki Kawagoe, Daisuke |
| author_facet | Imagawa, Masaki Kawagoe, Daisuke |
| contents | We consider a boundary value problem of a stationary advection equation in a bounded domain with Lipschitz boundary. It is known to be well-posed in $L^p$-based function spaces for $1 < p < \infty$ under the separation condition of the inflow and the outflow boundaries. In this article, we provide another sufficient condition for the well-posedness with $1 \leq p \leq \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A revisit on well-posedness of a boundary value problem of a stationary advection equation without the separation condition Imagawa, Masaki Kawagoe, Daisuke Analysis of PDEs Numerical Analysis 35F15, 35L02 We consider a boundary value problem of a stationary advection equation in a bounded domain with Lipschitz boundary. It is known to be well-posed in $L^p$-based function spaces for $1 < p < \infty$ under the separation condition of the inflow and the outflow boundaries. In this article, we provide another sufficient condition for the well-posedness with $1 \leq p \leq \infty$. |
| title | A revisit on well-posedness of a boundary value problem of a stationary advection equation without the separation condition |
| topic | Analysis of PDEs Numerical Analysis 35F15, 35L02 |
| url | https://arxiv.org/abs/2409.15603 |