Mass conservation and gelation for the Smoluchowski coagulation equation: a generalized moment approach
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910997998993408 |
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| author | Kimura, Masato Miyata, Hisanori |
| author_facet | Kimura, Masato Miyata, Hisanori |
| contents | The Smoluchowski coagulation equation (SCE) is a population balance model that describes the time evolution of cluster size distributions resulting from particle aggregation. Although it is formally a mass-conserving system, solutions may exhibit a gelation phenomenon-a sudden loss of mass-when the coagulation kernel grows superlinearly. In this paper, we rigorously analyze mass conservation and gelation for weak solutions to the SCE with inhomogeneous coagulation kernels. By introducing a generalized moment framework, we derive sharp sufficient conditions for both mass conservation and gelation, expressed in terms of the initial data and the properties of the coagulation kernel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08017 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mass conservation and gelation for the Smoluchowski coagulation equation: a generalized moment approach Kimura, Masato Miyata, Hisanori Analysis of PDEs 35R09 (Primary), 45K05 (Secondary) The Smoluchowski coagulation equation (SCE) is a population balance model that describes the time evolution of cluster size distributions resulting from particle aggregation. Although it is formally a mass-conserving system, solutions may exhibit a gelation phenomenon-a sudden loss of mass-when the coagulation kernel grows superlinearly. In this paper, we rigorously analyze mass conservation and gelation for weak solutions to the SCE with inhomogeneous coagulation kernels. By introducing a generalized moment framework, we derive sharp sufficient conditions for both mass conservation and gelation, expressed in terms of the initial data and the properties of the coagulation kernel. |
| title | Mass conservation and gelation for the Smoluchowski coagulation equation: a generalized moment approach |
| topic | Analysis of PDEs 35R09 (Primary), 45K05 (Secondary) |
| url | https://arxiv.org/abs/2506.08017 |