American Institute of Mathematical Sciences

Advanced
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

Xinfu Chen 1, , King-Yeung Lam 2, and  Yuan Lou 3,

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.
Keywords: exclusion, evolution of dispersal., Directed movement, competing species, reaction-diffusion-advection.
Mathematics Subject Classification: Primary: 35J57, 35B40; Secondary: 92D4.
Citation: Xinfu Chen, King-Yeung Lam, Yuan Lou. Corrigendum: Dynamics of a reaction-diffusion-advection model for two competing species. Discrete & 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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[5]

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

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[5]

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

[1]

Xinfu Chen, King-Yeung Lam, Yuan Lou. Dynamics of a reaction-diffusion-advection model for two competing species. Discrete & 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 & 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 & 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 & Continuous Dynamical Systems - B, 2021  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 & 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 & 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 & 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 & 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 & 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 & Continuous Dynamical Systems - B, 2012, 17 (1) : 221-243. doi: 10.3934/dcdsb.2012.17.221
[11]

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
[12]

Hao Wang, Katherine Dunning, James J. Elser, Yang Kuang. Daphnia species invasion, competitive exclusion, and chaotic coexistence. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 481-493. doi: 10.3934/dcdsb.2009.12.481
[13]

Elena Trofimchuk, Sergei Trofimchuk. Admissible wavefront speeds for a single species reaction-diffusion equation with delay. Discrete & Continuous Dynamical Systems, 2008, 20 (2) : 407-423. doi: 10.3934/dcds.2008.20.407
[14]

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
[15]

Rafael Bravo De La Parra, Luis Sanz. A discrete model of competing species sharing a parasite. Discrete & Continuous Dynamical Systems - B, 2020, 25 (6) : 2121-2142. doi: 10.3934/dcdsb.2019204
[16]

Frédéric Grognard, Frédéric Mazenc, Alain Rapaport. Polytopic Lyapunov functions for persistence analysis of competing species. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 73-93. doi: 10.3934/dcdsb.2007.8.73
[17]

Zhen-Hui Bu, Zhi-Cheng Wang. Curved fronts of monostable reaction-advection-diffusion equations in space-time periodic media. Communications on Pure & Applied Analysis, 2016, 15 (1) : 139-160. doi: 10.3934/cpaa.2016.15.139
[18]

Shi-Liang Wu, Wan-Tong Li, San-Yang Liu. Exponential stability of traveling fronts in monostable reaction-advection-diffusion equations with non-local delay. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 347-366. doi: 10.3934/dcdsb.2012.17.347
[19]

José-Francisco Rodrigues, João Lita da Silva. On a unilateral reaction-diffusion system and a nonlocal evolution obstacle problem. Communications on Pure & Applied Analysis, 2004, 3 (1) : 85-95. doi: 10.3934/cpaa.2004.3.85
[20]

Robert Stephen Cantrell, Chris Cosner, Yuan Lou. Evolution of dispersal and the ideal free distribution. Mathematical Biosciences & Engineering, 2010, 7 (1) : 17-36. doi: 10.3934/mbe.2010.7.17

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (48)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences