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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/2409.17974 |
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| _version_ | 1866913520188129280 |
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| author | Jang, Jiwoong Tran, Hung V. |
| author_facet | Jang, Jiwoong Tran, Hung V. |
| contents | Here, we study a discrete Coagulation-Fragmentation equation with a multiplicative coagulation kernel and a constant fragmentation kernel, which is critical. We apply the discrete Bernstein transform to the original Coagulation-Fragmentation equation to get two new singular Hamilton-Jacobi equations and use viscosity solution methods to analyze them. We obtain well-posedness, regularity, and long-time behaviors of the viscosity solutions to the Hamilton-Jacobi equations in certain ranges, which imply the well-posedness and long-time behaviors of mass-conserving solutions to the Coagulation-Fragmentation equation. The results obtained provide some definitive answers to a conjecture posed in [11,10], and are counterparts to those for the continuous case studied in [32]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discrete Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel Jang, Jiwoong Tran, Hung V. Analysis of PDEs Here, we study a discrete Coagulation-Fragmentation equation with a multiplicative coagulation kernel and a constant fragmentation kernel, which is critical. We apply the discrete Bernstein transform to the original Coagulation-Fragmentation equation to get two new singular Hamilton-Jacobi equations and use viscosity solution methods to analyze them. We obtain well-posedness, regularity, and long-time behaviors of the viscosity solutions to the Hamilton-Jacobi equations in certain ranges, which imply the well-posedness and long-time behaviors of mass-conserving solutions to the Coagulation-Fragmentation equation. The results obtained provide some definitive answers to a conjecture posed in [11,10], and are counterparts to those for the continuous case studied in [32]. |
| title | Discrete Coagulation-Fragmentation equations with multiplicative coagulation kernel and constant fragmentation kernel |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.17974 |