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Asymptotic behavior for a reaction-diffusion population model with delay
1. | Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010 |
2. | Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, United States |
References:
[1] |
S. Ai, Traveling wave fronts for generalized Fisher equations with spatio-temporal delays, J. Differential Equations, 232 (2007), 104-133.
doi: 10.1016/j.jde.2006.08.015. |
[2] |
M. V. Bartuccelli and S. A. Gourley, A Population model with time-dependent delay, Math. Comput. Modelling, 26 (1997), 13-30.
doi: 10.1016/S0895-7177(97)00237-9. |
[3] |
N. F. Britton, Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model, SIAM J. Appl. Math., 50 (1990), 1663-1688.
doi: 10.1137/0150099. |
[4] |
K. Deng, On a nonlocal reaction-diffusion population model, Discrete Contin. Dyn. Syst. Ser. B, 9 (2008), 65-73.
doi: 10.3934/dcdsb.2008.9.65. |
[5] |
S. A. Gourley and N. F. Briton, On a modified Volterra population equation with diffusion, Nonlinear Anal., 21 (1993), 389-395.
doi: 10.1016/0362-546X(93)90082-4. |
[6] |
Y. Kyrychko, S. A. Gourley and M. V. Bartuccelli, Comparison and convergence to equlibrium in a nonlocal delayed reaction-diffusion model on an infinite domain, Discrete Contin. Dyn. Syst. Ser. B, 5 (2005), 1015-1026.
doi: 10.3934/dcdsb.2005.5.1015. |
[7] |
R. Laister, Global asymptotic behavior in some functional parabolic equations, Nonlinear Anal., 50 (2002), 347-361.
doi: 10.1016/S0362-546X(01)00766-0. |
[8] |
C. Ou and J. Wu, Traveling wavefronts in a delayed food-limited population model, SIAM J. Math. Anal., 39 (2007), 103-125.
doi: 10.1137/050638011. |
[9] |
M. Protter and H. Weinberger, Maximum Priciples in Differential Equations, Prentice-Hall Inc, New Jersey, 1967. |
[10] |
R. Redlinger, Existence theorems for semilinear parabolic systems with functionals, Nonlinear Anal., 8 (1984), 667-682.
doi: 10.1016/0362-546X(84)90011-7. |
[11] |
R. Redlinger, On Volterra's population equation with diffusion, SIAM J. Math. Anal., 16 (1985), 135-142.
doi: 10.1137/0516008. |
[12] |
S. Ruan and D. Xiao, Stability of steady states and existence of travelling waves in a vector-disease model, Proc. Royal Soc. Edinburgh. Ser. A, 134 (2004), 991-1011.
doi: 10.1017/S0308210500003590. |
[13] |
A. Schiaffino, On a diffusion Volterra equation, Nonlinear Anal., 3 (1979), 595-600.
doi: 10.1016/0362-546X(79)90088-9. |
[14] |
Z-C. Wang, W-T. Li and S. Ruan, Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay, J. Differential Equations, 238 (2007), 153-200.
doi: 10.1016/j.jde.2007.03.025. |
[15] |
J. Wu and X-Q. Zhao, Permanence and convergence in multi-species competition systems with delay, Trans. Amer. Math. Soc., 126 (1998), 1709-1714.
doi: 10.1090/S0002-9939-98-04522-5. |
show all references
References:
[1] |
S. Ai, Traveling wave fronts for generalized Fisher equations with spatio-temporal delays, J. Differential Equations, 232 (2007), 104-133.
doi: 10.1016/j.jde.2006.08.015. |
[2] |
M. V. Bartuccelli and S. A. Gourley, A Population model with time-dependent delay, Math. Comput. Modelling, 26 (1997), 13-30.
doi: 10.1016/S0895-7177(97)00237-9. |
[3] |
N. F. Britton, Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model, SIAM J. Appl. Math., 50 (1990), 1663-1688.
doi: 10.1137/0150099. |
[4] |
K. Deng, On a nonlocal reaction-diffusion population model, Discrete Contin. Dyn. Syst. Ser. B, 9 (2008), 65-73.
doi: 10.3934/dcdsb.2008.9.65. |
[5] |
S. A. Gourley and N. F. Briton, On a modified Volterra population equation with diffusion, Nonlinear Anal., 21 (1993), 389-395.
doi: 10.1016/0362-546X(93)90082-4. |
[6] |
Y. Kyrychko, S. A. Gourley and M. V. Bartuccelli, Comparison and convergence to equlibrium in a nonlocal delayed reaction-diffusion model on an infinite domain, Discrete Contin. Dyn. Syst. Ser. B, 5 (2005), 1015-1026.
doi: 10.3934/dcdsb.2005.5.1015. |
[7] |
R. Laister, Global asymptotic behavior in some functional parabolic equations, Nonlinear Anal., 50 (2002), 347-361.
doi: 10.1016/S0362-546X(01)00766-0. |
[8] |
C. Ou and J. Wu, Traveling wavefronts in a delayed food-limited population model, SIAM J. Math. Anal., 39 (2007), 103-125.
doi: 10.1137/050638011. |
[9] |
M. Protter and H. Weinberger, Maximum Priciples in Differential Equations, Prentice-Hall Inc, New Jersey, 1967. |
[10] |
R. Redlinger, Existence theorems for semilinear parabolic systems with functionals, Nonlinear Anal., 8 (1984), 667-682.
doi: 10.1016/0362-546X(84)90011-7. |
[11] |
R. Redlinger, On Volterra's population equation with diffusion, SIAM J. Math. Anal., 16 (1985), 135-142.
doi: 10.1137/0516008. |
[12] |
S. Ruan and D. Xiao, Stability of steady states and existence of travelling waves in a vector-disease model, Proc. Royal Soc. Edinburgh. Ser. A, 134 (2004), 991-1011.
doi: 10.1017/S0308210500003590. |
[13] |
A. Schiaffino, On a diffusion Volterra equation, Nonlinear Anal., 3 (1979), 595-600.
doi: 10.1016/0362-546X(79)90088-9. |
[14] |
Z-C. Wang, W-T. Li and S. Ruan, Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay, J. Differential Equations, 238 (2007), 153-200.
doi: 10.1016/j.jde.2007.03.025. |
[15] |
J. Wu and X-Q. Zhao, Permanence and convergence in multi-species competition systems with delay, Trans. Amer. Math. Soc., 126 (1998), 1709-1714.
doi: 10.1090/S0002-9939-98-04522-5. |
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