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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2510.04270 |
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| _version_ | 1866909825705705472 |
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| author | Cristian, Iulia Velázquez, Juan J. L. |
| author_facet | Cristian, Iulia Velázquez, Juan J. L. |
| contents | We study a spatially inhomogeneous coagulation model that contains a transport term in the spatial variable. The transport term models the vertical motion of particles due to gravity, thereby incorporating their fall into the dynamics. Local existence of mass-conserving solutions for a class of coagulation rates for which in the spatially homogeneous case instantaneous gelation (i.e., instantaneous loss of mass) occurs has been proved in [Cristian-Niethammer-Velázquez, 2024]. In order to obtain some insight into how to prove global existence of solutions, we allow a fast sedimentation speed. For very fast sedimentation speed, we rigorously prove that solutions converge to a Dirac measure in the space variable. We also formally obtain in the limit a one-dimensional coagulation equation with diagonal kernel, i.e., only particles of the same size interact. This provides a physical intuition on how coagulation models with a diagonal kernel emerge. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mass concentration in a spatially inhomogeneous coagulation model with fast sedimentation Cristian, Iulia Velázquez, Juan J. L. Analysis of PDEs We study a spatially inhomogeneous coagulation model that contains a transport term in the spatial variable. The transport term models the vertical motion of particles due to gravity, thereby incorporating their fall into the dynamics. Local existence of mass-conserving solutions for a class of coagulation rates for which in the spatially homogeneous case instantaneous gelation (i.e., instantaneous loss of mass) occurs has been proved in [Cristian-Niethammer-Velázquez, 2024]. In order to obtain some insight into how to prove global existence of solutions, we allow a fast sedimentation speed. For very fast sedimentation speed, we rigorously prove that solutions converge to a Dirac measure in the space variable. We also formally obtain in the limit a one-dimensional coagulation equation with diagonal kernel, i.e., only particles of the same size interact. This provides a physical intuition on how coagulation models with a diagonal kernel emerge. |
| title | Mass concentration in a spatially inhomogeneous coagulation model with fast sedimentation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.04270 |