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Travelling wave solutions of a free boundary problem for a two-species competitive model
| 1. | Department of Mathematics, National Taiwan University, National Taiwan University, Taipei, 10617, Taiwan |
| 2. | Department of Mathematics, National Taiwan University, and National Center for Theoretical Sciences (Taipei Office), No. 1, Sec. 4, Roosevelt Road, Taipei, 10617 |
References:
| [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.
doi: 10.1137/090771089. |
| [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.
doi: 10.1016/j.jde.2011.02.011. |
| [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.
doi: 10.1007/BF00250432. |
| [4] |
D. Hilhorst, M. Mimura and R. Schätzle, Vanishing latent heat limit in a Stefan-like problem arising in biology, Nonlinear Anal. Real World Appl., 4 (2003), 261-285.
doi: 10.1016/S1468-1218(02)00009-3. |
| [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.
doi: 10.1016/j.nonrwa.2007.10.003. |
| [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.
doi: 10.1088/0951-7715/20/8/004. |
| [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.
doi: 10.1016/j.nonrwa.2009.04.001. |
| [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.
doi: 10.1007/BF03167042. |
| [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. |
show all references
References:
| [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.
doi: 10.1137/090771089. |
| [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.
doi: 10.1016/j.jde.2011.02.011. |
| [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.
doi: 10.1007/BF00250432. |
| [4] |
D. Hilhorst, M. Mimura and R. Schätzle, Vanishing latent heat limit in a Stefan-like problem arising in biology, Nonlinear Anal. Real World Appl., 4 (2003), 261-285.
doi: 10.1016/S1468-1218(02)00009-3. |
| [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.
doi: 10.1016/j.nonrwa.2007.10.003. |
| [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.
doi: 10.1088/0951-7715/20/8/004. |
| [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.
doi: 10.1016/j.nonrwa.2009.04.001. |
| [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.
doi: 10.1007/BF03167042. |
| [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. |
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