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Spreading speed and traveling waves for a two-species weak competition system with free boundary
1. | Department of Applied Mathematics, National University of Tainan, Tainan 700, Taiwan |
References:
[1] |
G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model, Networks and Heterogeneous Media (NHM), 7 (2012), 583-603.
doi: 10.3934/nhm.2012.7.583. |
[2] |
C.-H. Chang and C.-C. Chen, Travelling wave solutions of a free boundary problem for a two-species competitive model, Communications on Pure and Applied Analysis (CPAA), 12 (2012), 1065-1074.
doi: 10.3934/cpaa.2013.12.1065. |
[3] |
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing, SIAM Journal on Mathematical Analysis, 32 (2000), 778-800.
doi: 10.1137/S0036141099351693. |
[4] |
Y. Du and Z. Guo, Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II, Journal of Differential Equations, 250 (2011), 4336-4366.
doi: 10.1016/j.jde.2011.02.011. |
[5] |
Y. Du, Z. Guo and R. Peng, A diffusive logistic model with a free boundary in time-periodic environment, Journal of Functional Analysis, 265 (2013), 2089-2142.
doi: 10.1016/j.jfa.2013.07.016. |
[6] |
Y. Du and Z. Lin, Spreading-vanishing dichotomy in the diffsive logistic model with a free boundary, SIAM Journal on Mathematical Analysis, 42 (2010), 377-405. Correction in: http://turing.une.edu.au/~ydu/papers/DuLin-siam-10-correction.pdf.
doi: 10.1137/090771089. |
[7] |
Y. Du and Z. G. Lin, The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor, Discrete Cont. Dyn. Syst. (Ser. B), to appear. |
[8] |
Y. Du and B. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., to appear. |
[9] |
P. Feng and Z. Zhou, Finite traveling wave solutions in a degenerate cross-diffusion model for bacterial colony, Communications on Pure and Applied Analysis (CPAA), 6 (2007), 1145-1165.
doi: 10.3934/cpaa.2007.6.1145. |
[10] |
J.-S. Guo and C.-H. Wu, On a free boundary problem for a two-species weak competition system, Journal of Dynamics and Differential Equations, 24 (2012), 873-895.
doi: 10.1007/s10884-012-9267-0. |
[11] |
D. Hilhorst, M. Mimura and R. Schtzle, Vanishing latent heat limit in a Stefan-like problem arising in biology, Nonlinear Analysis: Real World Applications, 4 (2003), 261-285.
doi: 10.1016/S1468-1218(02)00009-3. |
[12] |
Y. Kaneko and Y. Yamada, A free boundary problem for a reaction-diffusion equation appearing in ecology, Adv. Math. Sci. Appl., 21 (2011) 467-492. |
[13] |
Z. G. Lin, A free boundary problem for a predator-prey model, Nonlinearity, 20 (2007), 1883-1892.
doi: 10.1088/0951-7715/20/8/004. |
[14] |
M. Mimura, Y. Yamada and S. Yotsutani, A free boundary problem in ecology, Japan Journal of Applied Mathematics, 2 (1985), 151-186.
doi: 10.1007/BF03167042. |
[15] |
M. Mimura, Y. Yamada and S. Yotsutani, Stability analysis for free boundary problems in ecology, Hiroshima Math. J., 16 (1986), 477-498. |
[16] |
M. Mimura, Y. Yamada and S. Yotsutani, Free boundary problems for some reaction-diffusion equations, Hiroshima Math. J., 17 (1987), 241-280. |
[17] |
R. Peng and X.-Q. Zhao, The diffusive logistic model with a free boundary and seasonal succession, Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 33 (2013), 2007-2031.
doi: 10.3934/dcds.2013.33.2007. |
[18] |
M. M. Tang and P. C. Fife, Propagating fronts for competing species equations with diffusion, Archive for Rational Mechanics and Analysis, 73 (1980), 69-77.
doi: 10.1007/BF00283257. |
[19] |
M. X. Wang, On some free boundary problems of the prey-predator model, preprint, arXiv:1301.2063. |
show all references
References:
[1] |
G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model, Networks and Heterogeneous Media (NHM), 7 (2012), 583-603.
doi: 10.3934/nhm.2012.7.583. |
[2] |
C.-H. Chang and C.-C. Chen, Travelling wave solutions of a free boundary problem for a two-species competitive model, Communications on Pure and Applied Analysis (CPAA), 12 (2012), 1065-1074.
doi: 10.3934/cpaa.2013.12.1065. |
[3] |
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing, SIAM Journal on Mathematical Analysis, 32 (2000), 778-800.
doi: 10.1137/S0036141099351693. |
[4] |
Y. Du and Z. Guo, Spreading-vanishing dichotomy in a diffusive logistic model with a free boundary, II, Journal of Differential Equations, 250 (2011), 4336-4366.
doi: 10.1016/j.jde.2011.02.011. |
[5] |
Y. Du, Z. Guo and R. Peng, A diffusive logistic model with a free boundary in time-periodic environment, Journal of Functional Analysis, 265 (2013), 2089-2142.
doi: 10.1016/j.jfa.2013.07.016. |
[6] |
Y. Du and Z. Lin, Spreading-vanishing dichotomy in the diffsive logistic model with a free boundary, SIAM Journal on Mathematical Analysis, 42 (2010), 377-405. Correction in: http://turing.une.edu.au/~ydu/papers/DuLin-siam-10-correction.pdf.
doi: 10.1137/090771089. |
[7] |
Y. Du and Z. G. Lin, The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor, Discrete Cont. Dyn. Syst. (Ser. B), to appear. |
[8] |
Y. Du and B. Lou, Spreading and vanishing in nonlinear diffusion problems with free boundaries, J. Eur. Math. Soc., to appear. |
[9] |
P. Feng and Z. Zhou, Finite traveling wave solutions in a degenerate cross-diffusion model for bacterial colony, Communications on Pure and Applied Analysis (CPAA), 6 (2007), 1145-1165.
doi: 10.3934/cpaa.2007.6.1145. |
[10] |
J.-S. Guo and C.-H. Wu, On a free boundary problem for a two-species weak competition system, Journal of Dynamics and Differential Equations, 24 (2012), 873-895.
doi: 10.1007/s10884-012-9267-0. |
[11] |
D. Hilhorst, M. Mimura and R. Schtzle, Vanishing latent heat limit in a Stefan-like problem arising in biology, Nonlinear Analysis: Real World Applications, 4 (2003), 261-285.
doi: 10.1016/S1468-1218(02)00009-3. |
[12] |
Y. Kaneko and Y. Yamada, A free boundary problem for a reaction-diffusion equation appearing in ecology, Adv. Math. Sci. Appl., 21 (2011) 467-492. |
[13] |
Z. G. Lin, A free boundary problem for a predator-prey model, Nonlinearity, 20 (2007), 1883-1892.
doi: 10.1088/0951-7715/20/8/004. |
[14] |
M. Mimura, Y. Yamada and S. Yotsutani, A free boundary problem in ecology, Japan Journal of Applied Mathematics, 2 (1985), 151-186.
doi: 10.1007/BF03167042. |
[15] |
M. Mimura, Y. Yamada and S. Yotsutani, Stability analysis for free boundary problems in ecology, Hiroshima Math. J., 16 (1986), 477-498. |
[16] |
M. Mimura, Y. Yamada and S. Yotsutani, Free boundary problems for some reaction-diffusion equations, Hiroshima Math. J., 17 (1987), 241-280. |
[17] |
R. Peng and X.-Q. Zhao, The diffusive logistic model with a free boundary and seasonal succession, Discrete and Continuous Dynamical Systems - Series A (DCDS-A), 33 (2013), 2007-2031.
doi: 10.3934/dcds.2013.33.2007. |
[18] |
M. M. Tang and P. C. Fife, Propagating fronts for competing species equations with diffusion, Archive for Rational Mechanics and Analysis, 73 (1980), 69-77.
doi: 10.1007/BF00283257. |
[19] |
M. X. Wang, On some free boundary problems of the prey-predator model, preprint, arXiv:1301.2063. |
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