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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.28194 |
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| _version_ | 1866912988263350272 |
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| author | Franco, Eugenia Kepka, Bernhard |
| author_facet | Franco, Eugenia Kepka, Bernhard |
| contents | In this paper we study a two-component coagulation equation that models the aggregation of rouleaux in blood. We consider product kernels that have homogeneity $2$ and we characterize the initial data that lead to gelation. We prove that, when gelation occurs, the solution to the two-component coagulation equation localizes along a direction of the space of cluster as $ t $ approaches the gelation time $0 < T_* < \infty $. The localization direction is determined by the initial datum. We also prove that the solution converges to a self-similar solution along the direction of localization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28194 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long-time behaviour of rouleau formation models Franco, Eugenia Kepka, Bernhard Analysis of PDEs Mathematical Physics 92-10, 35R09, 82C21 In this paper we study a two-component coagulation equation that models the aggregation of rouleaux in blood. We consider product kernels that have homogeneity $2$ and we characterize the initial data that lead to gelation. We prove that, when gelation occurs, the solution to the two-component coagulation equation localizes along a direction of the space of cluster as $ t $ approaches the gelation time $0 < T_* < \infty $. The localization direction is determined by the initial datum. We also prove that the solution converges to a self-similar solution along the direction of localization. |
| title | Long-time behaviour of rouleau formation models |
| topic | Analysis of PDEs Mathematical Physics 92-10, 35R09, 82C21 |
| url | https://arxiv.org/abs/2603.28194 |