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Traveling wave solutions in an integro-differential competition model
1. | Institute of Applied Mathematics, College of Science, Northwest A & F University, Yangling, Shaanxi 712100, China |
2. | Department of Mathematics, University of Louisville, Louisville, KY 40292 |
References:
[1] |
D. Aronson, The asymptotic speed of propagation of a simple epidemic, in "Nonlinear Diffusion" (eds. W. Fitzgibbon and H. Walker) (NSF-CBMS Regional Conf. Nonlinear Diffusion Equations, Univ. Houston, Houton, TX, 1976), Res. Notes Math., 14, Pitman, London, (1977), 1-23. |
[2] |
P. W. Bates, P. C. Fife, X. Ren and X. Wang, Traveling waves in a convolution model for phase transition, Arch. Rational. Mech. Anal., 138 (1997), 105-136. |
[3] |
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. |
[4] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speeds and linear determinancy for two-species competition models, J. Math. Biol., 45 (2002), 219-233.
doi: 10.1007/s002850200144. |
[5] |
B. Li, M. A. Lewis and H. F. Weinberger, Existence of traveling waves for integral recursions with nonmonotone growth functions, J. Math. Biol., 58 (2009), 323-338.
doi: 10.1007/s00285-008-0175-1. |
[6] |
W.-T. Li, G. Lin and S. Ruan, Existence of travelling wave solutions in delayed reaction-diffusion systems with application to diffusion-competition systems, Nonlinearity, 19 (2006), 1253-1273.
doi: 10.1088/0951-7715/19/6/003. |
[7] |
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. |
[8] |
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. |
[9] |
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. |
[10] |
K. Müller, "Investigations on the Organic Drift in North Swedish Streams," Tech. Report 34, Institute of Freshwater Research, Drottningholm, Sweden, 1954. |
[11] |
K. Müller, Stream drift as a chronobiological phenomenon in running water ecosystems, Ann. Rev. Eco. Sys., 5 (1974), 309-323.
doi: 10.1146/annurev.es.05.110174.001521. |
[12] |
J. D. Murray, "Mathematical Biology I: An Introduction," Third edition, Interdisciplinary Applied Mathematics, 17, Springer-Verlag, New York, 2002. |
[13] |
J. D. Murray, "Mathematical Biology II: Spatial Models and Biomedical Applications," Third edition, Interdisciplinary Applied Mathematics, 18, Springer-Verlag, New York, 2003. |
[14] |
A. Nilsson, Coleoptera from a Malaise-trap placed across a coastal stream in northern Sweden, Fauna Norrlandica, 3 (1981), 1-9. |
[15] |
A. Okubo and S. Levin, "Diffusion and Ecological Problems: Modern Perspectives," Second edition, Interdisciplinary Applied Mathematics, 14, Springer-Verlag, New York, 2001. |
[16] |
W. D. Pearson and R. H. Kramer, Drift and production of two aquatic insects in a mountain stream, Ecol. Monogr., 42 (1972), 365-385.
doi: 10.2307/1942214. |
[17] |
T. Roos, Studies on upstream migration in adult streamdwelling insects,, Inst. Freshwater Res. Drottningholm, (): 167.
|
[18] |
W. Rudin, "Functional Analysis," Second edition, International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. |
[19] |
N. Shigesada and K. Kawasaki, "Biological Invasions: Theory and Practice," Oxford University Press, Oxford, 1997. |
[20] |
M. M. Tang and P. Fife, Propagating fronts for competing species equations with diffusion, Arch. Ration. Mech. Anal., 73 (1980), 69-77.
doi: 10.1007/BF00283257. |
[21] |
D. Tilman and P. Kareiva, "Spatial Ecology," Princeton University Press, Princeton, New Jersey, 1997. |
[22] |
D. Volkov and R. Lui, Spreading speed and travelling wave solutions of a partially sedentary population, IMA. J. Appl. Math., 72 (2007), 801-816.
doi: 10.1093/imamat/hxm025. |
[23] |
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. |
[24] |
L. Zhang, "Traveling Wave Solutions and Periodic Solutions for Several Classes of Nonlinear Population Models," Ph.D thesis, Sichuan University, 2011. |
show all references
References:
[1] |
D. Aronson, The asymptotic speed of propagation of a simple epidemic, in "Nonlinear Diffusion" (eds. W. Fitzgibbon and H. Walker) (NSF-CBMS Regional Conf. Nonlinear Diffusion Equations, Univ. Houston, Houton, TX, 1976), Res. Notes Math., 14, Pitman, London, (1977), 1-23. |
[2] |
P. W. Bates, P. C. Fife, X. Ren and X. Wang, Traveling waves in a convolution model for phase transition, Arch. Rational. Mech. Anal., 138 (1997), 105-136. |
[3] |
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. |
[4] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speeds and linear determinancy for two-species competition models, J. Math. Biol., 45 (2002), 219-233.
doi: 10.1007/s002850200144. |
[5] |
B. Li, M. A. Lewis and H. F. Weinberger, Existence of traveling waves for integral recursions with nonmonotone growth functions, J. Math. Biol., 58 (2009), 323-338.
doi: 10.1007/s00285-008-0175-1. |
[6] |
W.-T. Li, G. Lin and S. Ruan, Existence of travelling wave solutions in delayed reaction-diffusion systems with application to diffusion-competition systems, Nonlinearity, 19 (2006), 1253-1273.
doi: 10.1088/0951-7715/19/6/003. |
[7] |
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. |
[8] |
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. |
[9] |
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. |
[10] |
K. Müller, "Investigations on the Organic Drift in North Swedish Streams," Tech. Report 34, Institute of Freshwater Research, Drottningholm, Sweden, 1954. |
[11] |
K. Müller, Stream drift as a chronobiological phenomenon in running water ecosystems, Ann. Rev. Eco. Sys., 5 (1974), 309-323.
doi: 10.1146/annurev.es.05.110174.001521. |
[12] |
J. D. Murray, "Mathematical Biology I: An Introduction," Third edition, Interdisciplinary Applied Mathematics, 17, Springer-Verlag, New York, 2002. |
[13] |
J. D. Murray, "Mathematical Biology II: Spatial Models and Biomedical Applications," Third edition, Interdisciplinary Applied Mathematics, 18, Springer-Verlag, New York, 2003. |
[14] |
A. Nilsson, Coleoptera from a Malaise-trap placed across a coastal stream in northern Sweden, Fauna Norrlandica, 3 (1981), 1-9. |
[15] |
A. Okubo and S. Levin, "Diffusion and Ecological Problems: Modern Perspectives," Second edition, Interdisciplinary Applied Mathematics, 14, Springer-Verlag, New York, 2001. |
[16] |
W. D. Pearson and R. H. Kramer, Drift and production of two aquatic insects in a mountain stream, Ecol. Monogr., 42 (1972), 365-385.
doi: 10.2307/1942214. |
[17] |
T. Roos, Studies on upstream migration in adult streamdwelling insects,, Inst. Freshwater Res. Drottningholm, (): 167.
|
[18] |
W. Rudin, "Functional Analysis," Second edition, International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. |
[19] |
N. Shigesada and K. Kawasaki, "Biological Invasions: Theory and Practice," Oxford University Press, Oxford, 1997. |
[20] |
M. M. Tang and P. Fife, Propagating fronts for competing species equations with diffusion, Arch. Ration. Mech. Anal., 73 (1980), 69-77.
doi: 10.1007/BF00283257. |
[21] |
D. Tilman and P. Kareiva, "Spatial Ecology," Princeton University Press, Princeton, New Jersey, 1997. |
[22] |
D. Volkov and R. Lui, Spreading speed and travelling wave solutions of a partially sedentary population, IMA. J. Appl. Math., 72 (2007), 801-816.
doi: 10.1093/imamat/hxm025. |
[23] |
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. |
[24] |
L. Zhang, "Traveling Wave Solutions and Periodic Solutions for Several Classes of Nonlinear Population Models," Ph.D thesis, Sichuan University, 2011. |
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