Global existence of measure-valued solutions to the multicomponent Smoluchowski coagulation equation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910910944116736 |
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| author | Ferreira, Marina A. Pirnes, Sakari |
| author_facet | Ferreira, Marina A. Pirnes, Sakari |
| contents | Global solutions to the multicomponent Smoluchowski coagulation equation are constructed for measure-valued initial data with minimal assumptions on the moments. The framework is based on an abstract formulation of the Arzelà-Ascoli theorem for uniform spaces. The result holds for a large class of coagulation rate kernels, satisfying a power-law upper bound with possibly different singularities at small-small, small-large and large-large coalescence pairs. This includes in particular both mass-conserving and gelling kernels, as well as interpolation kernels used in applications. We also provide short proofs of mass-conservation and gelation results for any weak solution, which extends previous results for one-component systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_10306 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global existence of measure-valued solutions to the multicomponent Smoluchowski coagulation equation Ferreira, Marina A. Pirnes, Sakari Analysis of PDEs Mathematical Physics 35Q82, 45K05 Global solutions to the multicomponent Smoluchowski coagulation equation are constructed for measure-valued initial data with minimal assumptions on the moments. The framework is based on an abstract formulation of the Arzelà-Ascoli theorem for uniform spaces. The result holds for a large class of coagulation rate kernels, satisfying a power-law upper bound with possibly different singularities at small-small, small-large and large-large coalescence pairs. This includes in particular both mass-conserving and gelling kernels, as well as interpolation kernels used in applications. We also provide short proofs of mass-conservation and gelation results for any weak solution, which extends previous results for one-component systems. |
| title | Global existence of measure-valued solutions to the multicomponent Smoluchowski coagulation equation |
| topic | Analysis of PDEs Mathematical Physics 35Q82, 45K05 |
| url | https://arxiv.org/abs/2504.10306 |