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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

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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

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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

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