Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures

Bruna M, Burger M, Ranetbauer H, Wolfram MT (2016)

Publication Type: Journal article

Publication year: 2016

Journal

Journal of Nonlinear Science Springer Verlag (Germany)

Publisher: Springer New York LLC

Book Volume: null

Pages Range: 1-33

Issue: null

DOI: 10.1007/s00332-016-9348-z

Abstract

In this paper, we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived in Bruna and Chapman (J Chem Phys 137:204116-1–204116-16, 2012a) from a stochastic system of interacting Brownian particles using the method of matched asymptotic expansions. The resulting cross-diffusion system is valid in the limit of small volume fraction of particles. While the system has a gradient flow structure in the symmetric case of all particles having the same size and diffusivity, this is not valid in general. We discuss local stability and global existence for the symmetric case using the gradient flow structure and entropy variable techniques. For the general case, we introduce the concept of an asymptotic gradient flow structure and show how it can be used to study the behavior close to equilibrium. Finally, we illustrate the behavior of the model with various numerical simulations.

Authors with CRIS profile

Martin Burger

Involved external institutions

University of Oxford GB United Kingdom (GB) Österreichische Akademie der Wissenschaften AT Austria (AT) Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE)

How to cite

APA:

Bruna, M., Burger, M., Ranetbauer, H., & Wolfram, M.-T. (2016). Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures. Journal of Nonlinear Science, null, 1-33. https://dx.doi.org/10.1007/s00332-016-9348-z

MLA:

Bruna, Maria, et al. "Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures." Journal of Nonlinear Science null (2016): 1-33.

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