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arXiv · 2403.06464

Cross-Diffusion Theory for Overcrowding Dispersal in Interacting Species System

Noureddine Igbida
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Abstract

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.

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Noureddine Igbida. 2024-03-11. Cross-Diffusion Theory for Overcrowding Dispersal in Interacting Species System. https://arxiv.org/abs/2403.06464

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