October  2011, 16(3): 973-984. doi: 10.3934/dcdsb.2011.16.973

Existence of traveling wavefront for discrete bistable competition model

1. 

Department of Applied Mathematics, National Chung Hsing University, 250, Kuo Kuang Road, Taichung 402, Taiwan

Received  September 2010 Revised  January 2011 Published  June 2011

We study traveling wavefront solutions for a two-component competition system on a one-dimensional lattice. We combine the monotonic iteration method with a truncation to obtain the existence of the traveling wavefront solution.
Citation: Chin-Chin Wu. Existence of traveling wavefront for discrete bistable competition model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 973-984. doi: 10.3934/dcdsb.2011.16.973
References:
[1]

Arch. Rational Mech. Anal., 189 (2008), 189-236. doi: 10.1007/s00205-007-0103-3.  Google Scholar

[2]

Indiana Univ. Math. J., 33 (1984), 319-343. doi: 10.1512/iumj.1984.33.33018.  Google Scholar

[3]

J. Differential Equations, 44 (1982), 343-364. doi: 10.1016/0022-0396(82)90001-8.  Google Scholar

[4]

J. S. Guo and C. H. Wu, Traveling wave front for a two-component lattice dynamical system arising in competition models,, preprint., ().   Google Scholar

[5]

J. Differential Equations, 250 (2011), 3504-3533. doi: 10.1016/j.jde.2010.12.004.  Google Scholar

[6]

Numerical and Applied Mathematics, Part II (Paris, 1988), Baltzer, Basel, (1989), 687-692.  Google Scholar

[7]

Bulletin of Math. Biology, 60 (1998), 435-448. doi: 10.1006/bulm.1997.0008.  Google Scholar

[8]

Nonlinear Anal., 28 (1997), 145-164.  Google Scholar

[9]

SIAM J. Appl. Math., 47 (1987), 556-572. doi: 10.1137/0147038.  Google Scholar

[10]

Proc. R. Soc. Lond. B, 238 (1989), 113-125. doi: 10.1098/rspb.1989.0070.  Google Scholar

[11]

Arch. Rational Mech. Anal., 73 (1980), 69-77. doi: 10.1007/BF00283257.  Google Scholar

show all references

References:
[1]

Arch. Rational Mech. Anal., 189 (2008), 189-236. doi: 10.1007/s00205-007-0103-3.  Google Scholar

[2]

Indiana Univ. Math. J., 33 (1984), 319-343. doi: 10.1512/iumj.1984.33.33018.  Google Scholar

[3]

J. Differential Equations, 44 (1982), 343-364. doi: 10.1016/0022-0396(82)90001-8.  Google Scholar

[4]

J. S. Guo and C. H. Wu, Traveling wave front for a two-component lattice dynamical system arising in competition models,, preprint., ().   Google Scholar

[5]

J. Differential Equations, 250 (2011), 3504-3533. doi: 10.1016/j.jde.2010.12.004.  Google Scholar

[6]

Numerical and Applied Mathematics, Part II (Paris, 1988), Baltzer, Basel, (1989), 687-692.  Google Scholar

[7]

Bulletin of Math. Biology, 60 (1998), 435-448. doi: 10.1006/bulm.1997.0008.  Google Scholar

[8]

Nonlinear Anal., 28 (1997), 145-164.  Google Scholar

[9]

SIAM J. Appl. Math., 47 (1987), 556-572. doi: 10.1137/0147038.  Google Scholar

[10]

Proc. R. Soc. Lond. B, 238 (1989), 113-125. doi: 10.1098/rspb.1989.0070.  Google Scholar

[11]

Arch. Rational Mech. Anal., 73 (1980), 69-77. doi: 10.1007/BF00283257.  Google Scholar

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