On measure-valued solutions for a structured population model with transfers
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916795514880000 |
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| author | Magal, Pierre Raoul, Gaël |
| author_facet | Magal, Pierre Raoul, Gaël |
| contents | We consider a transfer operator where two interacting cells carrying non-negative traits transfer a random fraction of their trait to each other. These transfers can lead to population having singular distributions in trait. We extend the definition of the transfer operator to non-negative measures with a finite second moment, and we discuss the regularity of the fixed distributions of that transfer operator. Finally, we consider a dynamic transfer model where an initial population distribution is affected by a transfer operator: we prove the existence and uniqueness of mild measure-valued solutions for that Cauchy problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13225 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On measure-valued solutions for a structured population model with transfers Magal, Pierre Raoul, Gaël Analysis of PDEs We consider a transfer operator where two interacting cells carrying non-negative traits transfer a random fraction of their trait to each other. These transfers can lead to population having singular distributions in trait. We extend the definition of the transfer operator to non-negative measures with a finite second moment, and we discuss the regularity of the fixed distributions of that transfer operator. Finally, we consider a dynamic transfer model where an initial population distribution is affected by a transfer operator: we prove the existence and uniqueness of mild measure-valued solutions for that Cauchy problem. |
| title | On measure-valued solutions for a structured population model with transfers |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.13225 |