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 & Continuous Dynamical Systems - A, 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.  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.   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.  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.  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., (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.  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.   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.  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.  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., (1983).   Google Scholar

[1]

Dan Wei, Shangjiang Guo. Qualitative analysis of a Lotka-Volterra competition-diffusion-advection system. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2599-2623. doi: 10.3934/dcdsb.2020197

[2]

Wei-Jian Bo, Guo Lin, Shigui Ruan. Traveling wave solutions for time periodic reaction-diffusion systems. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4329-4351. doi: 10.3934/dcds.2018189

[3]

Yizhuo Wang, Shangjiang Guo. A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1627-1652. doi: 10.3934/dcdsb.2018223

[4]

Nabahats Dib-Baghdadli, Rabah Labbas, Tewfik Mahdjoub, Ahmed Medeghri. On some reaction-diffusion equations generated by non-domiciliated triatominae, vectors of Chagas disease. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2021004

[5]

Jumpei Inoue, Kousuke Kuto. On the unboundedness of the ratio of species and resources for the diffusive logistic equation. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2441-2450. doi: 10.3934/dcdsb.2020186

[6]

Michel Chipot, Mingmin Zhang. On some model problem for the propagation of interacting species in a special environment. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020401

[7]

Shanshan Chen, Junping Shi, Guohong Zhang. Spatial pattern formation in activator-inhibitor models with nonlocal dispersal. Discrete & Continuous Dynamical Systems - B, 2021, 26 (4) : 1843-1866. doi: 10.3934/dcdsb.2020042

[8]

Guo-Bao Zhang, Ruyun Ma, Xue-Shi Li. Traveling waves of a Lotka-Volterra strong competition system with nonlocal dispersal. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 587-608. doi: 10.3934/dcdsb.2018035

[9]

Simone Cacace, Maurizio Falcone. A dynamic domain decomposition for the eikonal-diffusion equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 109-123. doi: 10.3934/dcdss.2016.9.109

[10]

Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367

[11]

Kin Ming Hui, Soojung Kim. Asymptotic large time behavior of singular solutions of the fast diffusion equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5943-5977. doi: 10.3934/dcds.2017258

[12]

Meiqiao Ai, Zhimin Zhang, Wenguang Yu. First passage problems of refracted jump diffusion processes and their applications in valuing equity-linked death benefits. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021039

[13]

Vo Anh Khoa, Thi Kim Thoa Thieu, Ekeoma Rowland Ijioma. On a pore-scale stationary diffusion equation: Scaling effects and correctors for the homogenization limit. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2451-2477. doi: 10.3934/dcdsb.2020190

2019 Impact Factor: 1.338

Metrics

  • PDF downloads (36)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]