References
- P. W. Bates, On some nonlocal evolution equations arising in materials science, In: Nonlinear dynamics and evolution equations (Ed. by H. Brunner, X. Zhao and X. Zou), pp. 13-52, Fields Inst. Commun. 48, AMS, Providence, 2006.
- P. W. Bates, P. C. Fife, X. Ren, and X. Wang, Traveling waves in a convolution model for phase transitions, Arch. Rational Mech. Anal. 138 (1997), no. 2, 105-136. https://doi.org/10.1007/s002050050037
- J. Carr and A. Chmaj, Uniqueness of travelling waves for nonlocal monostable equations, Proc. Amer. Math. Soc. 132 (2004), no. 8, 2433-2439. https://doi.org/10.1090/S0002-9939-04-07432-5
- X. Chen, Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations, Adv. Differential Equations 2 (1997), no. 1, 125-160.
- J. Coville and L. Dupaigne, Propagation speed of travelling fronts in non local reaction-diffusion equations, Nonlinear Anal. 60 (2005), no. 5, 797-819. https://doi.org/10.1016/j.na.2003.10.030
- J. Coville and L. Dupaigne, On a non-local equation arising in population dynamics, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), no. 4, 727-755. https://doi.org/10.1017/S0308210504000721
- S. A. Gourley and J. Wu, Delayed non-local diffusive systems in biological invasion and disease spread, In: Nonlinear dynamics and evolution equations (Ed. by H. Brunner, X. Zhao and X. Zou), pp. 137-200, Fields Inst. Commun. 48, AMS, Providence, 2006.
- L. Hopf, Introduction to Differential Equations of Physics, Dover, New York, 1948.
- Y. Jin and X. Q. Zhao, Spatial dynamics of a periodic population model with dispersal, Nonlinearity 22 (2009), no. 5, 1167-1189. https://doi.org/10.1088/0951-7715/22/5/011
- W. T. Li, Y. Sun, and Z. C. Wang, Entire solutions in the Fisher-KPP equation with nonlocal dispersal, Nonlinear Anal. Real World Appl. 11 (2010), no. 4, 2302-2313. https://doi.org/10.1016/j.nonrwa.2009.07.005
- X. Liang and X. Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math. 60 (2007), no. 1, 1-40. https://doi.org/10.1002/cpa.20154
- G. Lin and S. Ruan, Traveling wave solutions for delayed reaction-diffusion systems and applications to Lotka-Volterra competition-diffusion models with distributed delays, J. Dynam. Diff. Eqns., in press, DOI: 10.1007/s10884-014-9355-4.
- J. D. Murray, Mathematical Biology, Springer, Berlin-Heidelberg-New York, 1993.
- S. Pan, Traveling wave fronts of delayed non-local diffusion systems without quasimonotonicity, J. Math. Anal. Appl. 346 (2008), no. 2, 415-424. https://doi.org/10.1016/j.jmaa.2008.05.057
- S. Pan, W. T. Li, and G. Lin, Travelling wave fronts in nonlocal delayed reaction-diffusion systems and applications, Z. Angew. Math. Phys. 60 (2009), no. 3, 377-392. https://doi.org/10.1007/s00033-007-7005-y
- S. Pan, W. T. Li, and G. Lin, Existence and stability of traveling wavefronts in a nonlocal diffusion equation with delay, Nonlinear Anal. 72 (2010), no. 6, 3150-3158. https://doi.org/10.1016/j.na.2009.12.008
- W. Shen and A. Zhang, Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats, J. Differential Equations 249 (2010), no. 4, 747-795. https://doi.org/10.1016/j.jde.2010.04.012
- N. Shigesada and K. Kawasaki, Biological Invasions: Theory and Practice, Oxford University Press, Oxford, 1997.
- H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems, AMS, Providence, RI, 1995.
- Y. Sun, W. T. Li, and Z. C. Wang, Traveling waves for a nonlocal anisotropic dispersal equation with monostable nonlinearity, Nonlinear Anal. 74 (2011), no. 3, 814-826. https://doi.org/10.1016/j.na.2010.09.032
- S. Wu and S. Liu, Traveling waves for delayed non-local diffusion equations with crossing-monostability, Appl. Math. Comput. 217 (2010), no. 4, 1435-1444. https://doi.org/10.1016/j.amc.2009.05.056
- J. Xia, Z. Yu, and R. Yuan, Traveling waves of a competitive Lotka-Volterra model with nonlocal diffusion and time delays, Acta Math. Appl. Sin. 34 (2011), no. 6, 1082-1093.
- Z. Xu and P. Weng, Traveling waves in a convolution model with infinite distributed delay and non-monotonicity, Nonlinear Anal. Real World Appl. 12 (2011), no. 1, 633-647. https://doi.org/10.1016/j.nonrwa.2010.07.006
- Z. Yu and R. Yuan, Travelling wave solutions in nonlocal reaction-diffusion systems with delays and applications, ANZIAM J. 51 (2009), no. 1, 49-66. https://doi.org/10.1017/S1446181109000406
- Z. Yu and R. Yuan, Travelling wave solutions in non-local convolution diffusive competitive-cooperative systems, IMA J. Appl. Math. 76 (2011), no. 4, 493-513. https://doi.org/10.1093/imamat/hxq048
- G. Zhang, W. T. Li, and G. Lin, Traveling waves in delayed predator-prey systems with nonlocal diffusion and stage structure, Math. Comput. Modelling 49 (2009), no. 5-6, 1021-1029. https://doi.org/10.1016/j.mcm.2008.09.007
- G. Zhang, W. T. Li, and Z. C. Wang, Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity, J. Differential Equations 252 (2012), no. 9, 5096-5124. https://doi.org/10.1016/j.jde.2012.01.014
Cited by
- Traveling wave solutions of a nonlocal dispersal predator–prey model with spatiotemporal delay vol.69, pp.6, 2018, https://doi.org/10.1007/s00033-018-1041-7
- Minimal wave speed in a dispersal predator–prey system with delays vol.2018, pp.1, 2018, https://doi.org/10.1186/s13661-018-0966-2