Cross-Diffusion Theory for Overcrowding Dispersal in Interacting Species System
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917673882877952 |
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| author | Igbida, Noureddine |
| author_facet | Igbida, Noureddine |
| contents | This work introduces a new class of cross-diffusion systems for studying overcrowding dispersal of two species. The approach, based on proximal minimization energy through a minimum flow process, offers a potential generalization of existing segregation models. Unlike prior methods using PDEs or $W_2$-Wasserstein flows, it establishes a well-posed PDE framework for capturing the interplay between diffusion and concentration gradients. This framework has the potential to significantly improve our understanding of how cross-diffusion shapes spatial patterns, coexistence, and overall distribution of multiple species. Notably, for homogeneous cases, the approach definitely leads to a well-defined PDE grounded in a new general $H^{-1}$-theory specifically developed for overcrowding dispersal. This theory provides a robust foundation for further analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06464 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cross-Diffusion Theory for Overcrowding Dispersal in Interacting Species System Igbida, Noureddine Analysis of PDEs Optimization and Control This work introduces a new class of cross-diffusion systems for studying overcrowding dispersal of two species. The approach, based on proximal minimization energy through a minimum flow process, offers a potential generalization of existing segregation models. Unlike prior methods using PDEs or $W_2$-Wasserstein flows, it establishes a well-posed PDE framework for capturing the interplay between diffusion and concentration gradients. This framework has the potential to significantly improve our understanding of how cross-diffusion shapes spatial patterns, coexistence, and overall distribution of multiple species. Notably, for homogeneous cases, the approach definitely leads to a well-defined PDE grounded in a new general $H^{-1}$-theory specifically developed for overcrowding dispersal. This theory provides a robust foundation for further analysis. |
| title | Cross-Diffusion Theory for Overcrowding Dispersal in Interacting Species System |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2403.06464 |