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The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor
1. | School of Science and Technology, University of New England, Armidale, NSW 2351 |
2. | School of Mathematical Science, Yangzhou University, Yangzhou 225002 |
References:
[1] |
G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model, Netw. Heterog. Media, 7 (2012), 583-603.
doi: 10.3934/nhm.2012.7.583. |
[2] |
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., 32 (2000), 778-800.
doi: 10.1137/S0036141099351693. |
[3] |
R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, John Wiley& Sons Ltd, 2003.
doi: 10.1002/0470871296. |
[4] |
Y. Du and Z. M. Guo, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary II, J. Diff. Eqns., 250 (2011), 4336-4366.
doi: 10.1016/j.jde.2011.02.011. |
[5] |
Y. Du and Z. G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405.
doi: 10.1137/090771089. |
[6] |
Y. Du and L. Ma, Logistic type equations on $\mathbbR^N$ by a squeezing method involving boundary blow-up solutions, J. London Math. Soc., 64 (2001), 107-124.
doi: 10.1017/S0024610701002289. |
[7] |
J.-S. Guo and C.-H. Wu, On a free boundary problem for a two-species weak competition system, J. Dyn. Diff. Equat., 24 (2012), 873-895.
doi: 10.1007/s10884-012-9267-0. |
[8] |
Y. Kan-On, Fisher wave fronts for the Lotka-Volterra competition model with diffusion, Nonl. Anal. TMA, 28 (1997), 145-164.
doi: 10.1016/0362-546X(95)00142-I. |
[9] |
K. Kishimoto and H. F. Weinberger, The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains, J. Diff. Eqns., 58 (1985), 15-21.
doi: 10.1016/0022-0396(85)90020-8. |
[10] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, RI, 1968. |
[11] |
G. M. Lieberman, Second Order Parabolic Differential Equations, World Scientific, Singapore, 1996.
doi: 10.1142/3302. |
[12] |
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. |
[13] |
Y. Morita and K. Tachibana, An entire solution to the Lotka-Volterra competition-diffusion equations, SIAM J. Math. Anal., 40 (2009), 2217-2240.
doi: 10.1137/080723715. |
[14] |
C. V. Pao, Nonliear Parabolic and Elliptic Equations, Plenum Press, New York, 1992. |
[15] |
H. L. Smith, Monotone Dynamical Systems, American Math. Soc., Providence, 1995. |
[16] |
M. X. Wang, On some free boundary problems of the prey-predator model, J. Diff. Eqns., 256 (2014), 3365-3394.
doi: 10.1016/j.jde.2014.02.013. |
[17] |
J. F. Zhao and M. X. Wang, A free boundary problem for a predator-prey model with double free boundaries,, preprint., ().
|
show all references
References:
[1] |
G. Bunting, Y. Du and K. Krakowski, Spreading speed revisited: Analysis of a free boundary model, Netw. Heterog. Media, 7 (2012), 583-603.
doi: 10.3934/nhm.2012.7.583. |
[2] |
X. F. Chen and A. Friedman, A free boundary problem arising in a model of wound healing, SIAM J. Math. Anal., 32 (2000), 778-800.
doi: 10.1137/S0036141099351693. |
[3] |
R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, John Wiley& Sons Ltd, 2003.
doi: 10.1002/0470871296. |
[4] |
Y. Du and Z. M. Guo, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary II, J. Diff. Eqns., 250 (2011), 4336-4366.
doi: 10.1016/j.jde.2011.02.011. |
[5] |
Y. Du and Z. G. Lin, Spreading-vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM J. Math. Anal., 42 (2010), 377-405.
doi: 10.1137/090771089. |
[6] |
Y. Du and L. Ma, Logistic type equations on $\mathbbR^N$ by a squeezing method involving boundary blow-up solutions, J. London Math. Soc., 64 (2001), 107-124.
doi: 10.1017/S0024610701002289. |
[7] |
J.-S. Guo and C.-H. Wu, On a free boundary problem for a two-species weak competition system, J. Dyn. Diff. Equat., 24 (2012), 873-895.
doi: 10.1007/s10884-012-9267-0. |
[8] |
Y. Kan-On, Fisher wave fronts for the Lotka-Volterra competition model with diffusion, Nonl. Anal. TMA, 28 (1997), 145-164.
doi: 10.1016/0362-546X(95)00142-I. |
[9] |
K. Kishimoto and H. F. Weinberger, The spatial homogeneity of stable equilibria of some reaction-diffusion systems on convex domains, J. Diff. Eqns., 58 (1985), 15-21.
doi: 10.1016/0022-0396(85)90020-8. |
[10] |
O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, RI, 1968. |
[11] |
G. M. Lieberman, Second Order Parabolic Differential Equations, World Scientific, Singapore, 1996.
doi: 10.1142/3302. |
[12] |
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. |
[13] |
Y. Morita and K. Tachibana, An entire solution to the Lotka-Volterra competition-diffusion equations, SIAM J. Math. Anal., 40 (2009), 2217-2240.
doi: 10.1137/080723715. |
[14] |
C. V. Pao, Nonliear Parabolic and Elliptic Equations, Plenum Press, New York, 1992. |
[15] |
H. L. Smith, Monotone Dynamical Systems, American Math. Soc., Providence, 1995. |
[16] |
M. X. Wang, On some free boundary problems of the prey-predator model, J. Diff. Eqns., 256 (2014), 3365-3394.
doi: 10.1016/j.jde.2014.02.013. |
[17] |
J. F. Zhao and M. X. Wang, A free boundary problem for a predator-prey model with double free boundaries,, preprint., ().
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