Cross-Diffusion Theory for Overcrowding Dispersal in Interacting Species System

2024/03/11 by Noureddine Igbida, Igbida, Noureddine · 1 citation
Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2403.06464

openalex publication_date 2024/03/11 · openalex created_date 2024/03/13 · openalex updated_date 2026/07/28

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 W₂-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.

Cited by

• On a Cross-Diffusion System with Independent Drifts and no Self-Diffusion: The Existence of Totally Mixed Solutions

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