Segregation effects and gap formation in cross-diffusion models

Burger M, Carrillo JA, Pietschmann JF, Schmidtchen M (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Interfaces and Free Boundaries European Mathematical Society

Book Volume: 22

Pages Range: 175-203

Journal Issue: 2

DOI: 10.4171/IFB/438

Abstract

In this paper we analyse a class of nonlinear cross-diffusion systems for two species with local repulsive interactions that exhibit a formal gradient flow structure with respect to the Wasserstein metric. We show that systems where the population pressure is given by a function of the total population are critical with respect to cross-diffusion perturbations. This criticality is showcased by proving that adding an extra cross-diffusion term that breaks the symmetry of the population pressure in the system leads to completely different behaviours, namely segregation or mixing, depending on the sign of the perturbation. We show these results at the level of the minimisers of the associated free energy functionals. We also analyse certain implications for the gradient flow systems of the associated PDEs and present a numerical exploration of the time evolution of these phenomena.

Authors with CRIS profile

Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

University of Oxford

United Kingdom (GB) Technische Universität Chemnitz

Germany (DE) Imperial College London / The Imperial College of Science, Technology and Medicine

United Kingdom (GB)

How to cite

APA:

Burger, M., Carrillo, J.A., Pietschmann, J.-F., & Schmidtchen, M. (2020). Segregation effects and gap formation in cross-diffusion models. Interfaces and Free Boundaries, 22(2), 175-203. https://dx.doi.org/10.4171/IFB/438

MLA:

Burger, Martin, et al. "Segregation effects and gap formation in cross-diffusion models." Interfaces and Free Boundaries 22.2 (2020): 175-203.

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