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Applicable Analysis
An International Journal
Volume 89, 2010 - Issue 7: Analysis and Applications of PDEs in Biomathematics
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Original Articles

Reaction–diffusion models with large advection coefficients

Andriy Bezuglyy Department of Mathematics, Ohio State University, Columbus, OH 43210, USA
&
Yuan Lou Department of Mathematics, Ohio State University, Columbus, OH 43210, USACorrespondence[email protected]
Pages 983-1004 | Received 28 Sep 2009, Accepted 09 Nov 2009, Published online: 15 Jun 2010

Citations (24)

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Isabel Averill, Yuan Lou & Dan Munther. (2012) On several conjectures from evolution of dispersal. Journal of Biological Dynamics 6:2, pages 117-130.
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Articles from other publishers (23)

Xiaoqing He & Liu Liu. (2022) On the Conjecture of the Role of Advection in a Two-Species Competition-Diffusion Model. SIAM Journal on Applied Dynamical Systems 21:3, pages 1663-1685.
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Wenyi Qin & Peng Zhou. (2022) A REVIEW ON THE DYNAMICS OF TWO SPECIES COMPETITIVE ODE AND PARABOLIC SYSTEMS. Journal of Applied Analysis & Computation 12:5, pages 2075-2109.
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Li Ma & De Tang. (2020) Existence and Stability of Stationary States of a Reaction–Diffusion-Advection Model for Two Competing Species. International Journal of Bifurcation and Chaos 30:05, pages 2050065.
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Chang-Hong Wu. (2018) Biased movement and the ideal free distribution in some free boundary problems. Journal of Differential Equations 265:9, pages 4251-4282.
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Willian Cintra, Cristian Morales-Rodrigo & Antonio Suárez. (2018) Coexistence states in a cross-diffusion system of a predator–prey model with predator satiation term. Mathematical Models and Methods in Applied Sciences 28:11, pages 2131-2159.
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De Tang & Li Ma. (2018) Dynamical behavior of a general reaction–diffusion–advection model for two competing species. Computers & Mathematics with Applications 75:4, pages 1128-1142.
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Yin-Liang Huang & Chang-Hong Wu. (2017) Positive steady states of reaction–diffusion–advection competition models in periodic environment. Journal of Mathematical Analysis and Applications 453:2, pages 724-745.
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Min Zhu, Xiaofei Guo & Zhigui Lin. (2017) The risk index for an SIR epidemic model and spatial spreading of the infectious disease. Mathematical Biosciences and Engineering 14:5/6, pages 1565-1583.
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Yoshio YAMADA & Yusuke YOSHIDA. (2016) Asymptotic Behavior of Solutions for Semilinear Volterra Diffusion Equations with Spatial Inhomogeneity and Advection. Tokyo Journal of Mathematics 39:1.
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Kousuke Kuto & Tohru Tsujikawa. (2015) Limiting structure of steady-states to the Lotka–Volterra competition model with large diffusion and advection. Journal of Differential Equations 258:5, pages 1801-1858.
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King-Yeung Lam & Wei-Ming Ni. (2014) Advection-mediated competition in general environments. Journal of Differential Equations 257:9, pages 3466-3500.
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Yong-Jung Kim, Ohsang Kwon & Fang Li. (2013) Global asymptotic stability and the ideal free distribution in a starvation driven diffusion. Journal of Mathematical Biology 68:6, pages 1341-1370.
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King-Yeung Lam & Yuan Lou. (2013) Evolution of conditional dispersal: evolutionarily stable strategies in spatial models. Journal of Mathematical Biology 68:4, pages 851-877.
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Chris Cosner. (2014) Reaction-diffusion-advection models for the effects and evolution of dispersal. Discrete & Continuous Dynamical Systems - A 34:5, pages 1701-1745.
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Hailiang Liu & Hui Yu. (2014) Entropy/energy stable schemes for evolutionary dispersal models. Journal of Computational Physics 256, pages 656-677.
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Yong-Jung Kim, Ohsang Kwon & Fang Li. (2013) Evolution of Dispersal Toward Fitness. Bulletin of Mathematical Biology 75:12, pages 2474-2498.
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Robert Stephen Cantrell, Chris Cosner, Yuan Lou & Chao Xie. (2013) Random dispersal versus fitness-dependent dispersal. Journal of Differential Equations 254:7, pages 2905-2941.
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Robert Stephen Cantrell, Chris Cosner & Yuan Lou. (2011) Evolutionary stability of ideal free dispersal strategies in patchy environments. Journal of Mathematical Biology 65:5, pages 943-965.
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Song Liang & Yuan Lou. (2012) On the dependence of population size upon random dispersal rate. Discrete and Continuous Dynamical Systems - Series B 17:8, pages 2771-2788.
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Xinfu Chen, King-Yeung Lam & Yuan Lou. (2012) Dynamics of a reaction-diffusion-advection model for two competing species. Discrete and Continuous Dynamical Systems 32:11, pages 3841-3859.
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Lee Altenberg. (2012) Resolvent positive linear operators exhibit the reduction phenomenon. Proceedings of the National Academy of Sciences 109:10, pages 3705-3710.
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King-Yeung Lam. (2012) Limiting Profiles of Semilinear Elliptic Equations with Large Advection in Population Dynamics II. SIAM Journal on Mathematical Analysis 44:3, pages 1808-1830.
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King-Yeung Lam. (2011) Concentration phenomena of a semilinear elliptic equation with large advection in an ecological model. Journal of Differential Equations 250:1, pages 161-181.
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