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Spreading speeds and traveling wave solutions in cooperative integral-differential systems
1. | Department of Mathematics, University of Louisville, Louisville, KY 40292 |
2. | School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281 |
3. | School of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, United States |
References:
[1] |
S. Fedotov, Front propagation into an unstable state of reaction-transport systems, Phys. Rev. Lett., 86 (2001), 926-929.
doi: 10.1103/PhysRevLett.86.926. |
[2] |
Y. Jin and X. -Q. Zhao, Spatial dynamics of a periodic population model with dispersal, Nonlinearity, 22 (2009), 1167-1189.
doi: 10.1088/0951-7715/22/5/011. |
[3] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speeds and linear conjecture for two-species competition models, J. Math. Biol., 45 (2002), 219-233.
doi: 10.1007/s002850200144. |
[4] |
B. Li, H. F. Weinberger and M. A. Lewis, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci., 196 (2005), 82-98.
doi: 10.1016/j.mbs.2005.03.008. |
[5] |
B. Li, Traveling wave solutions in partially degenerate cooperative reaction-diffusion systems, J. Diff. Eqs., 252 (2012), 4842-4861.
doi: 10.1016/j.jde.2012.01.018. |
[6] |
B. Li and L. Zhang, Travelling wave solutions in delayed cooperative systems, Nonlinearity, 24 (2011), 1759-1776.
doi: 10.1088/0951-7715/24/6/004. |
[7] |
X. Liang and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Commun. Pure Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
[8] |
X. Liang and X.-Q. Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, J. Funct. Anal., 259 (2010), 857-903.
doi: 10.1016/j.jfa.2010.04.018. |
[9] |
R. Lui, Biological growth and spread modeled by systems of recursions I. Mathematical theory, Math. Biosci., 93 (1989), 269-295.
doi: 10.1016/0025-5564(89)90026-6. |
[10] |
F. Lutscher, E. Pachepsky and M. A. Lewis, The effect of dispersal patterns on stream populations, SIAM Rev., 47 (2005), 749-772.
doi: 10.1137/050636152. |
[11] |
V. Méndez, T. Pujol and J. Fort, Dispersal probability distributions and the wave-front speed problem, Phys. Rev. E., 65 (2002), 041109/1-041109/6. |
[12] |
K. Meyer and B. Li, A spatial model of plants with an age-Structured seed bank and juvenile stage, SIAM. J. Appl. Math., 73 (2013), 1676-1702.
doi: 10.1137/120880501. |
[13] |
J. Medlock and M. Kot, Spreading disease: Integral-differential equations old and new, Math. Biosci., 184 (2003), 201-222.
doi: 10.1016/S0025-5564(03)00041-5. |
[14] |
D. Mollison, Dependence of epidemic and population velocities on basic parameters, Math. Biosci., 107 (1991), 255-287.
doi: 10.1016/0025-5564(91)90009-8. |
[15] |
S. Pan and G. Lin, Invasion traveling wave solutions of a competitive system with dispersal, Bound. Value Probl., 2012 (2012), 11pp.
doi: 10.1186/1687-2770-2012-120. |
[16] |
Y.-J. Sun, W.-T. Li and Z.-C. Wang, Traveling waves for a nonlocal anisotropic dispersal equation with monostable nonlinearity, Nonlinear Anal., 74 (2011), 814-826.
doi: 10.1016/j.na.2010.09.032. |
[17] |
H. F. Weinberger, M. A. Lewis and B. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol., 45 (2002), 183-218.
doi: 10.1007/s002850200145. |
[18] |
H. F. Weinberger, M. A. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol., 55 (2007), 207-222.
doi: 10.1007/s00285-007-0078-6. |
[19] |
Z.-X. Yu and R. Yuan, Travelling wave solutions in nonlocal reactiondiffusion systems with delays and applications, ANZIAM J., 51 (2009), 49-66.
doi: 10.1017/S1446181109000406. |
[20] |
L. Zhang and B. Li, Traveling waves in an integro-differential competition model, Discrete and Continuous Dynamical Systems-Series B, 17 (2012), 417-428.
doi: 10.3934/dcdsb.2012.17.417. |
show all references
References:
[1] |
S. Fedotov, Front propagation into an unstable state of reaction-transport systems, Phys. Rev. Lett., 86 (2001), 926-929.
doi: 10.1103/PhysRevLett.86.926. |
[2] |
Y. Jin and X. -Q. Zhao, Spatial dynamics of a periodic population model with dispersal, Nonlinearity, 22 (2009), 1167-1189.
doi: 10.1088/0951-7715/22/5/011. |
[3] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speeds and linear conjecture for two-species competition models, J. Math. Biol., 45 (2002), 219-233.
doi: 10.1007/s002850200144. |
[4] |
B. Li, H. F. Weinberger and M. A. Lewis, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci., 196 (2005), 82-98.
doi: 10.1016/j.mbs.2005.03.008. |
[5] |
B. Li, Traveling wave solutions in partially degenerate cooperative reaction-diffusion systems, J. Diff. Eqs., 252 (2012), 4842-4861.
doi: 10.1016/j.jde.2012.01.018. |
[6] |
B. Li and L. Zhang, Travelling wave solutions in delayed cooperative systems, Nonlinearity, 24 (2011), 1759-1776.
doi: 10.1088/0951-7715/24/6/004. |
[7] |
X. Liang and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Commun. Pure Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
[8] |
X. Liang and X.-Q. Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, J. Funct. Anal., 259 (2010), 857-903.
doi: 10.1016/j.jfa.2010.04.018. |
[9] |
R. Lui, Biological growth and spread modeled by systems of recursions I. Mathematical theory, Math. Biosci., 93 (1989), 269-295.
doi: 10.1016/0025-5564(89)90026-6. |
[10] |
F. Lutscher, E. Pachepsky and M. A. Lewis, The effect of dispersal patterns on stream populations, SIAM Rev., 47 (2005), 749-772.
doi: 10.1137/050636152. |
[11] |
V. Méndez, T. Pujol and J. Fort, Dispersal probability distributions and the wave-front speed problem, Phys. Rev. E., 65 (2002), 041109/1-041109/6. |
[12] |
K. Meyer and B. Li, A spatial model of plants with an age-Structured seed bank and juvenile stage, SIAM. J. Appl. Math., 73 (2013), 1676-1702.
doi: 10.1137/120880501. |
[13] |
J. Medlock and M. Kot, Spreading disease: Integral-differential equations old and new, Math. Biosci., 184 (2003), 201-222.
doi: 10.1016/S0025-5564(03)00041-5. |
[14] |
D. Mollison, Dependence of epidemic and population velocities on basic parameters, Math. Biosci., 107 (1991), 255-287.
doi: 10.1016/0025-5564(91)90009-8. |
[15] |
S. Pan and G. Lin, Invasion traveling wave solutions of a competitive system with dispersal, Bound. Value Probl., 2012 (2012), 11pp.
doi: 10.1186/1687-2770-2012-120. |
[16] |
Y.-J. Sun, W.-T. Li and Z.-C. Wang, Traveling waves for a nonlocal anisotropic dispersal equation with monostable nonlinearity, Nonlinear Anal., 74 (2011), 814-826.
doi: 10.1016/j.na.2010.09.032. |
[17] |
H. F. Weinberger, M. A. Lewis and B. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol., 45 (2002), 183-218.
doi: 10.1007/s002850200145. |
[18] |
H. F. Weinberger, M. A. Lewis and B. Li, Anomalous spreading speeds of cooperative recursion systems, J. Math. Biol., 55 (2007), 207-222.
doi: 10.1007/s00285-007-0078-6. |
[19] |
Z.-X. Yu and R. Yuan, Travelling wave solutions in nonlocal reactiondiffusion systems with delays and applications, ANZIAM J., 51 (2009), 49-66.
doi: 10.1017/S1446181109000406. |
[20] |
L. Zhang and B. Li, Traveling waves in an integro-differential competition model, Discrete and Continuous Dynamical Systems-Series B, 17 (2012), 417-428.
doi: 10.3934/dcdsb.2012.17.417. |
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