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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.01316 |
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| _version_ | 1866908512324419584 |
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| author | Barik, Prasanta K. da Costa, Fernando P. Pinto, João T. Sasportes, Rafael |
| author_facet | Barik, Prasanta K. da Costa, Fernando P. Pinto, João T. Sasportes, Rafael |
| contents | In this article, we discuss the continuous version of the generalized exchange-driven growth model which is a variant of the coagulation model in which a smaller size particle is detached from a bigger one and merges with another particle. This new model is a continuous extension of the generalized exchange-driven growth model originally formulated in a discrete context [4]. In this work, we examine the existence of weak solutions to the continuous version of the generalized exchange-driven growth model under a suitable reaction rate. Under an additional condition on the reaction rates, a uniqueness result is established. Finally, we prove that solutions satisfy the mass-conserving property and the conservation of the total number of particles for coagulation rates with linear bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The continuous version of the generalized exchange-driven growth model Barik, Prasanta K. da Costa, Fernando P. Pinto, João T. Sasportes, Rafael Analysis of PDEs In this article, we discuss the continuous version of the generalized exchange-driven growth model which is a variant of the coagulation model in which a smaller size particle is detached from a bigger one and merges with another particle. This new model is a continuous extension of the generalized exchange-driven growth model originally formulated in a discrete context [4]. In this work, we examine the existence of weak solutions to the continuous version of the generalized exchange-driven growth model under a suitable reaction rate. Under an additional condition on the reaction rates, a uniqueness result is established. Finally, we prove that solutions satisfy the mass-conserving property and the conservation of the total number of particles for coagulation rates with linear bounds. |
| title | The continuous version of the generalized exchange-driven growth model |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.01316 |