On inverse problems in multi-population aggregation models
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916733486366720 |
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| author | Li, Yuhan Liu, Hongyu Lo, Catharine W. K. |
| author_facet | Li, Yuhan Liu, Hongyu Lo, Catharine W. K. |
| contents | This paper focuses on inverse problems arising in studying multi-population aggregations. The goal is to reconstruct the diffusion coefficient, advection coefficient, and interaction kernels of the aggregation system, which characterize the dynamics of different populations. In the theoretical analysis of the physical setup, it is crucial to ensure non-negativity of solutions. To address this, we employ the high-order variation method and introduce modifications to the systems. Additionally, we propose a novel approach called transformative asymptotic technique that enables the recovery of the diffusion coefficient preceding the Laplace operator, presenting a pioneering method for this type of problems. Through these techniques, we offer comprehensive insights into the unique identifiability aspect of inverse problems associated with multi-population aggregation models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09837 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On inverse problems in multi-population aggregation models Li, Yuhan Liu, Hongyu Lo, Catharine W. K. Analysis of PDEs Populations and Evolution 35R30, 35B09, 35K45, 35Q92, 92-10, 92D25, 92D50, 35B10, 35C20 This paper focuses on inverse problems arising in studying multi-population aggregations. The goal is to reconstruct the diffusion coefficient, advection coefficient, and interaction kernels of the aggregation system, which characterize the dynamics of different populations. In the theoretical analysis of the physical setup, it is crucial to ensure non-negativity of solutions. To address this, we employ the high-order variation method and introduce modifications to the systems. Additionally, we propose a novel approach called transformative asymptotic technique that enables the recovery of the diffusion coefficient preceding the Laplace operator, presenting a pioneering method for this type of problems. Through these techniques, we offer comprehensive insights into the unique identifiability aspect of inverse problems associated with multi-population aggregation models. |
| title | On inverse problems in multi-population aggregation models |
| topic | Analysis of PDEs Populations and Evolution 35R30, 35B09, 35K45, 35Q92, 92-10, 92D25, 92D50, 35B10, 35C20 |
| url | https://arxiv.org/abs/2404.09837 |