Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit

• Published in: Journal of mathematical biology Vol. 83; no. 5; p. 58
• Main Authors: Brocchieri, Elisabetta, Corrias, Lucilla, Dietert, Helge, Kim, Yong-Jung
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2021; Springer Nature B.V; Springer
• Subjects: Analysis of PDEs; Applications of Mathematics; Boundary conditions; Competition; Diet; Diffusion; Diffusion rate; Evolution; Mathematical and Computational Biology; Mathematical models; Mathematics; Mathematics and Statistics; Population; Cross-diffusion; Entropy; Primary : 35B25, 35B40, 35K57, 35Q92, 92D25; Secondary 35B45, 35K45; Turing instability; Starvation-driven diffusion; starvation-driven diffusion; entropy

We rigorously prove the passage from a Lotka-Volterra reaction-diffusion system towards a cross-diffusion system at the fast reaction limit. The system models a competition of two species, where one species has a more diverse diet than the other. The resulting limit gives a cross-diffusion system of...