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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.08312 |
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| _version_ | 1866913617292558336 |
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| author | Bo, Lijun Huang, Yijie Yu, Xiang |
| author_facet | Bo, Lijun Huang, Yijie Yu, Xiang |
| contents | This paper studies the existence and uniqueness of a classical solution to a type of Robin boundary problems on the nonnegative orthant. We propose a new decomposition-homogenization method for the Robin boundary problem based on probabilistic representations, which leads to two auxiliary Robin boundary problems admitting some simplified probabilistic representations. The auxiliary probabilistic representations allow us to establish the existence of a unique classical solution to the original Robin boundary problem using some stochastic flow analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_08312 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A decomposition-homogenization method for Robin boundary problems on the nonnegative orthant Bo, Lijun Huang, Yijie Yu, Xiang Probability Analysis of PDEs This paper studies the existence and uniqueness of a classical solution to a type of Robin boundary problems on the nonnegative orthant. We propose a new decomposition-homogenization method for the Robin boundary problem based on probabilistic representations, which leads to two auxiliary Robin boundary problems admitting some simplified probabilistic representations. The auxiliary probabilistic representations allow us to establish the existence of a unique classical solution to the original Robin boundary problem using some stochastic flow analysis. |
| title | A decomposition-homogenization method for Robin boundary problems on the nonnegative orthant |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2306.08312 |