November  2014, 34(11): 4989-4995. doi: 10.3934/dcds.2014.34.4989

Corrigendum: Dynamics of a reaction-diffusion-advection model for two competing species

1. 

Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260

2. 

Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210, United States

3. 

Department of Mathematics, Mathematical Bioscience Institute, Ohio State University, Columbus, Ohio 43210

Received  December 2013 Revised  December 2013 Published  May 2014

We provide a corrected proof of [4, Theorem 2.2], which preserves the validity of the theorem exactly under those assumptions as stated in the original paper.
Citation: Xinfu Chen, King-Yeung Lam, Yuan Lou. Corrigendum: Dynamics of a reaction-diffusion-advection model for two competing species. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4989-4995. doi: 10.3934/dcds.2014.34.4989
References:
[1]

H. Amann and J. Lopez-Gomez, A priori bounds and multiple solutions for superlinear indefinite elliptic problems, J. Diff. Eqns., 146 (2002), 336-374. doi: 10.1006/jdeq.1998.3440.

[2]

F. Belgacem and C. Cosner, The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment, Canadian Appl. Math. Quarterly, 3 (1995), 379-397.

[3]

S. Cano-Casanova and J. Lopez-Gomez, Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems, J. Diff. Eqns., 178 (2002), 123-211. doi: 10.1006/jdeq.2000.4003.

[4]

X. Chen, K.-Y. Lam and Y. Lou, Dynamics of a reaction-diffusion-advection model for two competiting species, Discrete Cont. Dyn. Sys. A, 32 (2012), 3841-3859. doi: 10.3934/dcds.2012.32.3841.

[5]

D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equation of Second Order, $2^{nd}$ Ed., Springer-Verlag, Berlin, 1983.

show all references

References:
[1]

H. Amann and J. Lopez-Gomez, A priori bounds and multiple solutions for superlinear indefinite elliptic problems, J. Diff. Eqns., 146 (2002), 336-374. doi: 10.1006/jdeq.1998.3440.

[2]

F. Belgacem and C. Cosner, The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment, Canadian Appl. Math. Quarterly, 3 (1995), 379-397.

[3]

S. Cano-Casanova and J. Lopez-Gomez, Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems, J. Diff. Eqns., 178 (2002), 123-211. doi: 10.1006/jdeq.2000.4003.

[4]

X. Chen, K.-Y. Lam and Y. Lou, Dynamics of a reaction-diffusion-advection model for two competiting species, Discrete Cont. Dyn. Sys. A, 32 (2012), 3841-3859. doi: 10.3934/dcds.2012.32.3841.

[5]

D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equation of Second Order, $2^{nd}$ Ed., Springer-Verlag, Berlin, 1983.

[1]

Xinfu Chen, King-Yeung Lam, Yuan Lou. Dynamics of a reaction-diffusion-advection model for two competing species. Discrete and Continuous Dynamical Systems, 2012, 32 (11) : 3841-3859. doi: 10.3934/dcds.2012.32.3841

[2]

Chris Cosner. Reaction-diffusion-advection models for the effects and evolution of dispersal. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 1701-1745. doi: 10.3934/dcds.2014.34.1701

[3]

Bo Duan, Zhengce Zhang. A two-species weak competition system of reaction-diffusion-advection with double free boundaries. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 801-829. doi: 10.3934/dcdsb.2018208

[4]

Bo Duan, Zhengce Zhang. A reaction-diffusion-advection two-species competition system with a free boundary in heterogeneous environment. Discrete and Continuous Dynamical Systems - B, 2022, 27 (2) : 837-861. doi: 10.3934/dcdsb.2021067

[5]

Renhao Cui. Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate. Discrete and Continuous Dynamical Systems - B, 2021, 26 (6) : 2997-3022. doi: 10.3934/dcdsb.2020217

[6]

Mostafa Bendahmane, Kenneth H. Karlsen. Renormalized solutions of an anisotropic reaction-diffusion-advection system with $L^1$ data. Communications on Pure and Applied Analysis, 2006, 5 (4) : 733-762. doi: 10.3934/cpaa.2006.5.733

[7]

Danhua Jiang, Zhi-Cheng Wang, Liang Zhang. A reaction-diffusion-advection SIS epidemic model in a spatially-temporally heterogeneous environment. Discrete and Continuous Dynamical Systems - B, 2018, 23 (10) : 4557-4578. doi: 10.3934/dcdsb.2018176

[8]

Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅰ: Dirichlet and Neumann boundary conditions. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2357-2376. doi: 10.3934/cpaa.2017116

[9]

Anna Kostianko, Sergey Zelik. Inertial manifolds for 1D reaction-diffusion-advection systems. Part Ⅱ: periodic boundary conditions. Communications on Pure and Applied Analysis, 2018, 17 (1) : 285-317. doi: 10.3934/cpaa.2018017

[10]

Linfeng Mei, Xiaoyan Zhang. On a nonlocal reaction-diffusion-advection system modeling phytoplankton growth with light and nutrients. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 221-243. doi: 10.3934/dcdsb.2012.17.221

[11]

Chengxia Lei, Xinhui Zhou. Concentration phenomenon of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with spontaneous infection. Discrete and Continuous Dynamical Systems - B, 2022, 27 (6) : 3077-3100. doi: 10.3934/dcdsb.2021174

[12]

Baifeng Zhang, Guohong Zhang, Xiaoli Wang. Threshold dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey system. Discrete and Continuous Dynamical Systems - B, 2022, 27 (9) : 4969-4993. doi: 10.3934/dcdsb.2021260

[13]

Xu Rao, Guohong Zhang, Xiaoli Wang. A reaction-diffusion-advection SIS epidemic model with linear external source and open advective environments. Discrete and Continuous Dynamical Systems - B, 2022, 27 (11) : 6655-6677. doi: 10.3934/dcdsb.2022014

[14]

Kwangjoong Kim, Wonhyung Choi, Inkyung Ahn. Reaction-advection-diffusion competition models under lethal boundary conditions. Discrete and Continuous Dynamical Systems - B, 2022, 27 (9) : 4749-4767. doi: 10.3934/dcdsb.2021250

[15]

Roberto A. Saenz, Herbert W. Hethcote. Competing species models with an infectious disease. Mathematical Biosciences & Engineering, 2006, 3 (1) : 219-235. doi: 10.3934/mbe.2006.3.219

[16]

Hao Wang, Katherine Dunning, James J. Elser, Yang Kuang. Daphnia species invasion, competitive exclusion, and chaotic coexistence. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 481-493. doi: 10.3934/dcdsb.2009.12.481

[17]

Elena Trofimchuk, Sergei Trofimchuk. Admissible wavefront speeds for a single species reaction-diffusion equation with delay. Discrete and Continuous Dynamical Systems, 2008, 20 (2) : 407-423. doi: 10.3934/dcds.2008.20.407

[18]

Linda J. S. Allen, Vrushali A. Bokil. Stochastic models for competing species with a shared pathogen. Mathematical Biosciences & Engineering, 2012, 9 (3) : 461-485. doi: 10.3934/mbe.2012.9.461

[19]

Rafael Bravo De La Parra, Luis Sanz. A discrete model of competing species sharing a parasite. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : 2121-2142. doi: 10.3934/dcdsb.2019204

[20]

Frédéric Grognard, Frédéric Mazenc, Alain Rapaport. Polytopic Lyapunov functions for persistence analysis of competing species. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 73-93. doi: 10.3934/dcdsb.2007.8.73

2021 Impact Factor: 1.588

Metrics

  • PDF downloads (75)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]