Cross-diffusion models: Analytic and multiscale problems-Reference-Cited by-同舟云学术

Cross-diffusion models: Analytic and multiscale problems

Published:2018-10 Issue:11 Volume:28 Page:2097-2102
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Bellomo N.¹,Tao Y.²,Winkler M.³

Affiliation:

1. Politecnico di Torino and Collegio Carlo Alberto, Torino, Italy

2. Department of Applied Mathematics, Dong Hua University, Shanghai 200051, P. R. China

3. Institut für Mathematik, Universität Paderborn, 33098 Paderborn, Germany

Abstract

A presentation of a special issue on the derivation of cross-diffusion models and on the related analytical problems is proposed in this note. A brief introduction to motivations and recently published literature is presented in the first part. Subsequently, a concise description of the contents of the papers published in the issue follows. Finally, some ideas on possible research perspectives are proposed.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202518020025

Reference33 articles.

1. Cross-diffusion and traveling waves in porous-media flux-saturated Keller–Segel models

2. From a multiscale derivation of nonlinear cross-diffusion models to Keller–Segel models in a Navier–Stokes fluid

3. Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

4. A quest toward a mathematical theory of the dynamics of swarms

5. A degenerate chemotaxis system with flux limitation: Maximally extended solutions and absence of gradient blow-up

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