Entropic structure and duality for multiple species cross-diffusion systems

2016/09/27 by Thomas Lepoutre, Lepoutre, Thomas, Ayman Moussa +1 · 2 citations
Engineering · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Stability and Controllability of Differential Equations

paper · doi:10.48550/arxiv.1609.08503

openalex publication_date 2016/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with the existence of global weak solutions for a wide class of (multiple species) cross-diffusions systems. The existence is based on two different ingredients: an entropy estimate giving some gradient control and a duality estimate that gives naturally L² control. The proof relies on a semi-implicit scheme tailored for cross-diffusion systems firstly defined by the two authors and collaborators. These results are applied to models having an entropy relying on the detailed balance condition recently exhibited by Chen et. al.

Citations

• Boundedness of weak solutions to cross-diffusion systems from population\n dynamics

Cited by

• Stability of non-conservative cross diffusion model and approximation by stochastic particle systems
• Global strong solutions for the triangular Shigesada-Kawasaki-Teramoto cross-diffusion system in three dimensions and parabolic regularisation for increasing functions

Related

• Cross-diffusion systems with entropy structure
• The Shigesada-Kawasaki-Teramoto cross-diffusion system beyond detailed balance
• Entropy, Duality and Cross Diffusion
• Boundedness of weak solutions to cross-diffusion systems from population\n dynamics
• Cross-diffusion systems and fast-reaction limits