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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 |
[1] |
Kousuke Kuto, Yoshio Yamada. On limit systems for some population models with cross-diffusion. Discrete and Continuous Dynamical Systems - B, 2012, 17 (8) : 2745-2769. doi: 10.3934/dcdsb.2012.17.2745 |
[2] |
Mostafa Bendahmane, Kenneth H. Karlsen. Martingale solutions of stochastic nonlocal cross-diffusion systems. Networks and Heterogeneous Media, 2022 doi: 10.3934/nhm.2022024 |
[3] |
Anotida Madzvamuse, Hussaini Ndakwo, Raquel Barreira. Stability analysis of reaction-diffusion models on evolving domains: The effects of cross-diffusion. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 2133-2170. doi: 10.3934/dcds.2016.36.2133 |
[4] |
Anotida Madzvamuse, Raquel Barreira. Domain-growth-induced patterning for reaction-diffusion systems with linear cross-diffusion. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2775-2801. doi: 10.3934/dcdsb.2018163 |
[5] |
Robert Stephen Cantrell, Xinru Cao, King-Yeung Lam, Tian Xiang. A PDE model of intraguild predation with cross-diffusion. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3653-3661. doi: 10.3934/dcdsb.2017145 |
[6] |
Yuan Lou, Wei-Ming Ni, Yaping Wu. On the global existence of a cross-diffusion system. Discrete and Continuous Dynamical Systems, 1998, 4 (2) : 193-203. doi: 10.3934/dcds.1998.4.193 |
[7] |
Yuan Lou, Wei-Ming Ni, Shoji Yotsutani. Pattern formation in a cross-diffusion system. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1589-1607. doi: 10.3934/dcds.2015.35.1589 |
[8] |
Maxime Breden, Christian Kuehn, Cinzia Soresina. On the influence of cross-diffusion in pattern formation. Journal of Computational Dynamics, 2021, 8 (2) : 213-240. doi: 10.3934/jcd.2021010 |
[9] |
Yaru Hu, Jinfeng Wang. Dynamics of an SIRS epidemic model with cross-diffusion. Communications on Pure and Applied Analysis, 2022, 21 (1) : 315-336. doi: 10.3934/cpaa.2021179 |
[10] |
Yanxia Wu, Yaping Wu. Existence of traveling waves with transition layers for some degenerate cross-diffusion systems. Communications on Pure and Applied Analysis, 2012, 11 (3) : 911-934. doi: 10.3934/cpaa.2012.11.911 |
[11] |
Zheng Sun, José A. Carrillo, Chi-Wang Shu. An entropy stable high-order discontinuous Galerkin method for cross-diffusion gradient flow systems. Kinetic and Related Models, 2019, 12 (4) : 885-908. doi: 10.3934/krm.2019033 |
[12] |
Yuan Lou, Salomé Martínez, Wei-Ming Ni. On $3\times 3$ Lotka-Volterra competition systems with cross-diffusion. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 175-190. doi: 10.3934/dcds.2000.6.175 |
[13] |
Yaping Wu, Qian Xu. The existence and structure of large spiky steady states for S-K-T competition systems with cross-diffusion. Discrete and Continuous Dynamical Systems, 2011, 29 (1) : 367-385. doi: 10.3934/dcds.2011.29.367 |
[14] |
Hideki Murakawa. A relation between cross-diffusion and reaction-diffusion. Discrete and Continuous Dynamical Systems - S, 2012, 5 (1) : 147-158. doi: 10.3934/dcdss.2012.5.147 |
[15] |
Hirofumi Izuhara, Shunsuke Kobayashi. Spatio-temporal coexistence in the cross-diffusion competition system. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 919-933. doi: 10.3934/dcdss.2020228 |
[16] |
Yuan Lou, Wei-Ming Ni, Shoji Yotsutani. On a limiting system in the Lotka--Volterra competition with cross-diffusion. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 435-458. doi: 10.3934/dcds.2004.10.435 |
[17] |
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 |
[18] |
Daniel Ryan, Robert Stephen Cantrell. Avoidance behavior in intraguild predation communities: A cross-diffusion model. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1641-1663. doi: 10.3934/dcds.2015.35.1641 |
[19] |
Yi Li, Chunshan Zhao. Global existence of solutions to a cross-diffusion system in higher dimensional domains. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 185-192. doi: 10.3934/dcds.2005.12.185 |
[20] |
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 |
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