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May  2014, 19(3): 817-826. doi: 10.3934/dcdsb.2014.19.817

Traveling wave solutions of competitive models with free boundaries

1. 

Department of Mathematics, Tongji University, Shanghai, 200092, China

2. 

Department of Mathematics, Tongji University, Shanghai 200092

Received  July 2013 Revised  September 2013 Published  February 2014

We study two systems of reaction diffusion equations with monostable or bistable type of nonlinearities and with free boundaries. These systems are used as multi-species competitive model. For two-species models, we prove the existence of traveling wave solutions, each of which consists of two semi-waves intersecting at the free boundary. For three-species models, we also obtain some traveling wave solutions. In this case, however, every traveling wave solution consists of two semi-waves and one compactly supported wave in between, each intersecting with its neighbors at the free boundaries.
Citation: Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817
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show all references

References:
[1]

in Partial Differential Equations and Related Topics, Lecture Notes in Math., 446, Springer, Berlin, (1975), pp. 5-49.  Google Scholar

[2]

Adv. in Math., 30 (1978), 33-76. doi: 10.1016/0001-8708(78)90130-5.  Google Scholar

[3]

Commun. Pure Appl. Anal., 12 (2013), 1065-1074. doi: 10.3934/cpaa.2013.12.1065.  Google Scholar

[4]

Nonlinear Anal. Real World Appl., 5 (2004), 645-665. doi: 10.1016/j.nonrwa.2004.01.004.  Google Scholar

[5]

European J. Appl. Math., 10 (1999), 97-115. doi: 10.1017/S0956792598003660.  Google Scholar

[6]

SIAM J. Math. Anal., 42 (2010), 377-405. doi: 10.1137/090771089.  Google Scholar

[7]

Y. Du and B. D. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries,, J. Eur. Math. Soc., ().   Google Scholar

[8]

Japan J. Indust. Appl. Math., 18 (2001), 161-180. doi: 10.1007/BF03168569.  Google Scholar

[9]

Japan J. Appl. Math., 2 (1985), 151-186. doi: 10.1007/BF03167042.  Google Scholar

[10]

Hiroshima Math. J., 16 (1986), 477-498.  Google Scholar

[11]

Hiroshima Math. J., 17 (1987), 241-280.  Google Scholar

[12]

J. Math. Anal. Appl., 379 (2011), 150-170. doi: 10.1016/j.jmaa.2010.12.040.  Google Scholar

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