Free Access
Math. Model. Nat. Phenom.
Volume 10, Number 6, 2015
Nonlocal reaction-diffusion equations
Page(s) 142 - 162
Published online 02 October 2015
  1. H. Amann, Fixed point equations and nonlinea eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976), 620-709. [CrossRef] [MathSciNet] [Google Scholar]
  2. F. Andreu, J. M. Mazón, J. D. Rossi, J. Toledo, Nonlocal Diffusion Problems, Math. Surveys Monogr., Amer. Math. Soc., Providence, RI, 2010. [Google Scholar]
  3. N. Apreutesei, A. Ducrot and V. Volpert, Competition of species with intra-specific competition, Math. Model. Nat. Phenom. 3 (2008), 1-27. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  4. N. Apreutesei, N. Bessonov, V. Volpert and V. Vougalter, Spatial structures and generalized travelling waves for an integro-differential equation, Discrete Contin. Dynam. Syst. Ser. B. 13 (2010), 537-557. [Google Scholar]
  5. N. Apreutesei and V. Volpert, Properness and topological degree for nonlocal reaction-diffusion operators, Abstract Appl. Anal. (2011), 1-21. [Google Scholar]
  6. N. Apreutesei and V. Volpert, Existence of travelling waves for a class of integro-differential equations from population dynamics, Intl. Electron. J. Pure Appl. Math. 5 (2012), 53-67. [Google Scholar]
  7. N. Apreutesei and V. Volpert, Properness and topological degree for nonlocal integro-differential systems, Topol. Methods Nonlinear Anal. 43 (2014), 215-229. [Google Scholar]
  8. D. G. Aronson, The asymptotic speed of propagation of a simple epidemic, in “Nonlinear Diffusion”, eds. by W. E. Fitzgibbon and H. F. Walker, Research Notes in Math. 14, Pitman, London, 1977, pp. 1-23. [Google Scholar]
  9. P. W. Bates and A. Chmaj, An integrodifferential model for phase transitions: Stationary solution in higher space dimensions, J. Stat. Phys. 95 (1999), 1119-1139. [CrossRef] [Google Scholar]
  10. P. W. Bates and F. Chen, Spectral analysis of traveling waves for nonlocal evolution equations, SIAM J. Math. Anal. 38 (2006), 116-126. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. W. Bates, P.C. Fife, X. Ren and X. Wang, Traveling waves in a nonlocal model of phase transitions, Arch. Rat. Mech. Anal. 138 (1997), 105-136. [Google Scholar]
  12. P. W. Bates, J. Han and G. Zhao, On a nonlocal phase-field system, Nonlinear Anal. 64 (2006), 2251-2278. [CrossRef] [MathSciNet] [Google Scholar]
  13. P. W. Bates and G. Zhao, Existence, uniqueness and stability of stationary solution to a nonlocal evolution equation arising in population dispersal, J. Math. Anal. Appl. 332 (2007), 428-440. [CrossRef] [Google Scholar]
  14. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, New York, 2011. [Google Scholar]
  15. X. Chen, Existence, Uniqueness and asymptotic stability of traveling waves in nonlocal evolution equations, Adv. Differential Equations 2 (1997), 125-160. [MathSciNet] [Google Scholar]
  16. Z. Chen, B. Ermentrout and B. Mcleod, Traveling fronts for a class of non-local convolution differential equatons, Appl. Anal. 64 (1997), 235-253. [CrossRef] [Google Scholar]
  17. A. De Masi, E. Orlandi, E. Presutti and L. Triolo, Stability of the interface in a model of phase separation, Proc. Roy. Soc. Edinburgh 124A (1994), 1013-1022. [Google Scholar]
  18. T. Kato, Perturbation Theory for Linear Operators, Springer Verlag, New York, 1976. [Google Scholar]
  19. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, Berlin, 1981. [Google Scholar]
  20. W. Huang, Uniqueness of the bistable traveling wave for mutualist spaceies, J. Dynam. Differential Equations 13 (2001), 147-183. [CrossRef] [MathSciNet] [Google Scholar]
  21. H. J. Hupkes and S. M. Verduyn Lunel, Analysis of Newton’s method to compute travelling waves in discrete media, J. Dynam. Differential Equations 17 (2005), 523-572. [CrossRef] [MathSciNet] [Google Scholar]
  22. J. Mallet-Paret, The Fredholm alternative for functional differential equation of mixed type, J. Dynam. Differential Equations 11 (1999), 1-48. [CrossRef] [MathSciNet] [Google Scholar]
  23. J. Mallet-Paret, The global structure of traveling waves in spatially discrete dynamical systems, J. Dynam. Differential Equations 11 (1999), 49-127. [CrossRef] [MathSciNet] [Google Scholar]
  24. M. Miklavcic, Applied Functional Analysis and Partial Differential Equations, World Scientific, Singapore, 1998. [Google Scholar]
  25. A. Pazy, Asymptotic expansions of solutions of ordinary differential equations in Hilbert space, Arch. Rat. Mech. Anal. 24 (1967), 105-136. [CrossRef] [Google Scholar]
  26. S. Ruan, Spatial-temporal dynamics in nonlocal epidemiological models, in “Mathematics for Life Science and Medicine”, Vol. 2, Y. Takeuchi, K. Sato and Y. Iwasa (eds.), Springer-Verlag, New York, 2007, pp. 97-122. [Google Scholar]
  27. K. H. Schumacher, Traveling front solutions for integro-differential equation I, J. Reine Angew. Math. 316 (1980), 54-70. [MathSciNet] [Google Scholar]
  28. H. R. Thieme, Remarks on resolvent positive operators and their perturbation, Discrete Contin. Dynam. Syst. 4 (1998), 73-90. [Google Scholar]
  29. A. I. Volpert, Vi. A. Volpert and Vl. A. Volpert, Traveling Wave Solutions of Parabolic Systems, Translated from Russian by J. F. Heyda, Transl. Math. Monogr., Vol. 140, Amer. Math. Soc., Providence, 1994. [Google Scholar]
  30. H. F. Weinberger, Long-time behavior of a class of biological models, SIAM J. Math. Anal. 13 (1982), 353-396. [CrossRef] [MathSciNet] [Google Scholar]
  31. G. Zhao, Multidimensional periodic traveling waves in infinite cylinders, Discrete Contin. Dynam. Syst. 24 (2009), 1025-1045. [CrossRef] [Google Scholar]
  32. G. Zhao and S. Ruan, Existence, uniqueness and asymptotic stability of time periodic traveling waves for a periodic Lotka-Volterra competition system with diffusion, J. Math. Pures Appl. 95 (2011), 627-671. [CrossRef] [Google Scholar]
  33. G. Zhao and S. Ruan, Time periodic traveling wave solutions for periodic advection-reaction-diffusion systems, J. Differential Equations 257 (2014), 1078-1147. [CrossRef] [MathSciNet] [Google Scholar]

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