Steady States of Transport-Coagulation-Nucleation Models
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910048047857664 |
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| author | Delacour, Julia Doumic, Marie Moschella, Carmela Schmeiser, Christian |
| author_facet | Delacour, Julia Doumic, Marie Moschella, Carmela Schmeiser, Christian |
| contents | To model the dynamics of polymers formed through nucleation, elongated by polymerisation, shortened by depolymerisation and subject to aggregation reactions, we study a nonlinear integro-differential equation. Growth and shrinkage are described by transport terms, nucleation by a positive boundary condition, and aggregation by a Smoluchowski coagulation kernel. Our main result is the existence of steady states for the multiplicative coagulation kernel despite this kernel producing gelation in finite time for the pure coagulation equation. This is made possible by a sufficiently strong decay rate for large polymers. Beyond the existence result, the qualitative properties of the steady states are illustrated through explicit examples and numerical experiments. The analytical results connect the growth behaviour of the transport velocity and of the coagulation kernel to the decay properties of steady states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09751 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Steady States of Transport-Coagulation-Nucleation Models Delacour, Julia Doumic, Marie Moschella, Carmela Schmeiser, Christian Analysis of PDEs 35Q92, 82C22, 82D30, 82B40 To model the dynamics of polymers formed through nucleation, elongated by polymerisation, shortened by depolymerisation and subject to aggregation reactions, we study a nonlinear integro-differential equation. Growth and shrinkage are described by transport terms, nucleation by a positive boundary condition, and aggregation by a Smoluchowski coagulation kernel. Our main result is the existence of steady states for the multiplicative coagulation kernel despite this kernel producing gelation in finite time for the pure coagulation equation. This is made possible by a sufficiently strong decay rate for large polymers. Beyond the existence result, the qualitative properties of the steady states are illustrated through explicit examples and numerical experiments. The analytical results connect the growth behaviour of the transport velocity and of the coagulation kernel to the decay properties of steady states. |
| title | Steady States of Transport-Coagulation-Nucleation Models |
| topic | Analysis of PDEs 35Q92, 82C22, 82D30, 82B40 |
| url | https://arxiv.org/abs/2603.09751 |