doi: 10.3934/dcdss.20202i

Preface: Analysis of cross-diffusion systems

1. 

Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany

2. 

Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland

Published  January 2019

Citation: Michael Winkler, Dariusz Wrzosek. Preface: Analysis of cross-diffusion systems. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.20202i
[1]

Kousuke Kuto, Yoshio Yamada. On limit systems for some population models with cross-diffusion. Discrete & Continuous Dynamical Systems - B, 2012, 17 (8) : 2745-2769. doi: 10.3934/dcdsb.2012.17.2745

[2]

Anotida Madzvamuse, Hussaini Ndakwo, Raquel Barreira. Stability analysis of reaction-diffusion models on evolving domains: The effects of cross-diffusion. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 2133-2170. doi: 10.3934/dcds.2016.36.2133

[3]

Anotida Madzvamuse, Raquel Barreira. Domain-growth-induced patterning for reaction-diffusion systems with linear cross-diffusion. Discrete & Continuous Dynamical Systems - B, 2018, 23 (7) : 2775-2801. doi: 10.3934/dcdsb.2018163

[4]

Robert Stephen Cantrell, Xinru Cao, King-Yeung Lam, Tian Xiang. A PDE model of intraguild predation with cross-diffusion. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3653-3661. doi: 10.3934/dcdsb.2017145

[5]

Yuan Lou, Wei-Ming Ni, Yaping Wu. On the global existence of a cross-diffusion system. Discrete & Continuous Dynamical Systems - A, 1998, 4 (2) : 193-203. doi: 10.3934/dcds.1998.4.193

[6]

Yuan Lou, Wei-Ming Ni, Shoji Yotsutani. Pattern formation in a cross-diffusion system. Discrete & Continuous Dynamical Systems - A, 2015, 35 (4) : 1589-1607. doi: 10.3934/dcds.2015.35.1589

[7]

Yanxia Wu, Yaping Wu. Existence of traveling waves with transition layers for some degenerate cross-diffusion systems. Communications on Pure & Applied Analysis, 2012, 11 (3) : 911-934. doi: 10.3934/cpaa.2012.11.911

[8]

Yuan Lou, Salomé Martínez, Wei-Ming Ni. On $3\times 3$ Lotka-Volterra competition systems with cross-diffusion. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 175-190. doi: 10.3934/dcds.2000.6.175

[9]

Yaping Wu, Qian Xu. The existence and structure of large spiky steady states for S-K-T competition systems with cross-diffusion. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 367-385. doi: 10.3934/dcds.2011.29.367

[10]

Hideki Murakawa. A relation between cross-diffusion and reaction-diffusion. Discrete & Continuous Dynamical Systems - S, 2012, 5 (1) : 147-158. doi: 10.3934/dcdss.2012.5.147

[11]

Yuan Lou, Wei-Ming Ni, Shoji Yotsutani. On a limiting system in the Lotka--Volterra competition with cross-diffusion. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 435-458. doi: 10.3934/dcds.2004.10.435

[12]

Kousuke Kuto, Yoshio Yamada. Coexistence states for a prey-predator model with cross-diffusion. Conference Publications, 2005, 2005 (Special) : 536-545. doi: 10.3934/proc.2005.2005.536

[13]

Daniel Ryan, Robert Stephen Cantrell. Avoidance behavior in intraguild predation communities: A cross-diffusion model. Discrete & Continuous Dynamical Systems - A, 2015, 35 (4) : 1641-1663. doi: 10.3934/dcds.2015.35.1641

[14]

Yi Li, Chunshan Zhao. Global existence of solutions to a cross-diffusion system in higher dimensional domains. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 185-192. doi: 10.3934/dcds.2005.12.185

[15]

F. Berezovskaya, Erika Camacho, Stephen Wirkus, Georgy Karev. "Traveling wave'' solutions of Fitzhugh model with cross-diffusion. Mathematical Biosciences & Engineering, 2008, 5 (2) : 239-260. doi: 10.3934/mbe.2008.5.239

[16]

Shanbing Li, Jianhua Wu. Effect of cross-diffusion in the diffusion prey-predator model with a protection zone. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1539-1558. doi: 10.3934/dcds.2017063

[17]

Thomas Lepoutre, Salomé Martínez. Steady state analysis for a relaxed cross diffusion model. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 613-633. doi: 10.3934/dcds.2014.34.613

[18]

Lianzhang Bao, Wenjie Gao. Finite traveling wave solutions in a degenerate cross-diffusion model for bacterial colony with volume filling. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2813-2829. doi: 10.3934/dcdsb.2017152

[19]

Y. S. Choi, Roger Lui, Yoshio Yamada. Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 719-730. doi: 10.3934/dcds.2004.10.719

[20]

Y. S. Choi, Roger Lui, Yoshio Yamada. Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with weak cross-diffusion. Discrete & Continuous Dynamical Systems - A, 2003, 9 (5) : 1193-1200. doi: 10.3934/dcds.2003.9.1193

2017 Impact Factor: 0.561

Metrics

  • PDF downloads (15)
  • HTML views (67)
  • Cited by (0)

Other articles
by authors

[Back to Top]