`a`
Communications on Pure and Applied Analysis (CPAA)
 

Travelling wave solutions of a free boundary problem for a two-species competitive model
Pages: 1065 - 1074, Issue 2, March 2013

doi:10.3934/cpaa.2013.12.1065      Abstract        References        Full text (391.7K)           Related Articles

Chueh-Hsin Chang - Department of Mathematics, National Taiwan University, National Taiwan University, Taipei, 10617, Taiwan (email)
Chiun-Chuan Chen - Department of Mathematics, National Taiwan University, and National Center for Theoretical Sciences (Taipei Office), No. 1, Sec. 4, Roosevelt Road, Taipei, 10617, Taiwan (email)

1 Y. Du and Z. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405. Correction in: http://turing.une.edu.au/ ydu/papers/DuLin-siam-10-correction.pdf.       
2 Y. Du and Z. Guo, Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary II, J. Differential Equations, 250 (2011), 4336-4366.       
3 P. C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to traveling front solutions, Arch. Ration. Mech. Anal., 65 (1977), 335-361.       
4 D. Hilhorst, M. Mimura and R. Sch√§tzle, Vanishing latent heat limit in a Stefan-like problem arising in biology, Nonlinear Anal. Real World Appl., 4 (2003), 261-285.       
5 K. I. Kim and Z. Lin, A free boundary problem for a parabolic system describing an ecological model, Nonlinear Anal. Real World Appl., 10 (2009), 428-436.       
6 A. N. Kolmogorov, I. G. Petrovsky and N. S. Piskunov, Etude de l'equations de la diffusion avec croissance de la quantite de matiere et son application a un probleme biologique, Bull. Univ. Moscou S'er. Internat., A1 (1937), 1-26. English transl. in Dynamics of Curved Fronts, P. Pelc'e (ed.), Academic Press, 1988, 105-130.
7 Z. Lin, A free boundary problem for a predator-prey model, Nonlinearity, 20 (2007), 1883-1892.       
8 Z. Ling, Q. Tang and Z. Lin, A free boundary problem for two-species competitive model in ecology, Nonlinear Anal. Real World Appl., 11 (2010), 1775-1781.       
9 J. L. Lockwood, M. F. Hoopes and M. P. Marchetti, "Invasion Ecology," Blackwell Pub-lishing, Oxford, 2007.
10 M. Mimura, Y. Yamada and S. Yotsutani, A free boundary problem in ecology, Japan J. Appl. Math., 2 (1985), 151-186.       
11 M. Mimura, Y. Yamada and S. Yotsutani, Stability analysis for free boundary problems in ecology, Hiroshima Math. J., 16 (1986), 477-498.       
12 M. Mimura, Y. Yamada and S. Yotsutani, Free boundary problems for some reaction-diffusion equations, Hiroshima Math. J., 17 (1987), 241-280.       
13 N. Shigesada and K. Kawasaki, "Biological Invasions: Theory and Practice," Oxford Series in Ecology and Evolution, Oxford University Press, Oxford, 1997.
14 J. G. Skellam, Random dispersal in theoretical populations, Biometrika, 38 (1951), 196-218.       
15 A. I. Volpert, V. A. Volpert and V. A. Volpert, "Traveling Wave Solutions of Parabolic Systems," Translations of Mathematical Monographs, 140, Amer. Math. Soc., Providence, 1994.       

Go to top