Free Access
Math. Model. Nat. Phenom.
Volume 10, Number 6, 2015
Nonlocal reaction-diffusion equations
Page(s) 113 - 141
Published online 02 October 2015
  1. P. Bates, G. Zhao, Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal, J. Math. Anal. Appl., 332 (2007), 428-440. [CrossRef] [Google Scholar]
  2. H. Berestycki, J. Coville, H.-H. Vo, Nonlocal heterogeneous KPP equations inN, (2014) preprint. [Google Scholar]
  3. H. Berestycki, J. Coville, H-H Vo, Persistence criteria for populations with non-local dispersion, (2014), preprint. [Google Scholar]
  4. R. S. Cantrell, C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Series in Mathematical and Computational Biology, John Wiley and Sons, Chichester, UK, 2003. [Google Scholar]
  5. E. Chasseigne, M. Chaves, J. D. Rossi, Asymptotic behavior for nonlocal diffusion equations, J. Math. Pures Appl., 86 (2006), 271-291. [CrossRef] [Google Scholar]
  6. J. Coville, On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators, J. Differential Equations, 249 (2010), 2921-2953. [CrossRef] [MathSciNet] [Google Scholar]
  7. J. Coville, On uniqueness and monotonicity of solutions of non-local reaction diffusion equation, Annali di Matematica, 185(3) (2006), 461-485 [CrossRef] [MathSciNet] [Google Scholar]
  8. J. Coville, J. Dávila, S. Martínez, Existence and uniqueness of solutions to a nonlocal equation with monostable nonlinearity, SIAM J. Math. Anal., 39 (2008), 1693-1709. [CrossRef] [MathSciNet] [Google Scholar]
  9. J. Coville, J. Dávila, S. Martínez, Pulsating fronts for nonlocal dispersion and KPP nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), 179-223. [CrossRef] [MathSciNet] [Google Scholar]
  10. J. Coville, L. Dupaigne, Propagation speed of travelling fronts in non local reaction-diffusion equations, Nonlinear Analysis, 60 (2005), 797-819. [Google Scholar]
  11. C. Cortazar, M. Elgueta, J. D. Rossi, Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions, Israel J. of Math., 170 (2009), 53-60. [CrossRef] [Google Scholar]
  12. J. Fang, X.-Q. Zhao, Traveling waves for monotone semiflows with weak compactness, SIAM J. Math. Anal., 46 (2014), no. 6, 3678-3704. [CrossRef] [MathSciNet] [Google Scholar]
  13. P. Fife, Some nonclassical trends in parabolic and parabolic-like evolutions, Trends in nonlinear analysis, 153-191, Springer, Berlin, 2003. [Google Scholar]
  14. J. García-Melán, J. D. Rossi, On the principal eigenvalue of some nonlocal diffusion problems, J. Differential Equations, 246 (2009), 21-38. [CrossRef] [MathSciNet] [Google Scholar]
  15. J.S. Guo, X. Liang, The minimal speed of traveling fronts for Lotka-Volterra competition system, J. Dynam. Differential equations, 23 (2011), 353-363. [CrossRef] [MathSciNet] [Google Scholar]
  16. J.-S. Guo, C.-H. Wu, Traveling wave front for a two-component lattice dynamical system arising in competition models, J. Differential Equations, 252 (2012), no. 8, 4357-4391. [CrossRef] [MathSciNet] [Google Scholar]
  17. G. Hetzer, T. Nguyen, W. Shen, Coexistence and extinction in the Volterra-Lotka competition model with nonlocal dispersal, Commun. Pure Appl. Anal., 11 (2012), no. 5, 1699-1722. [CrossRef] [MathSciNet] [Google Scholar]
  18. Y. Hosono, The minimal speed of traveling frons for a diffusive Lotka-Volterra comptition model, Bull. Math. Biol. , 60 (1998), 435-448. [CrossRef] [Google Scholar]
  19. W. Huang, Problem on minimum wave speed for a Lotka-Volterra reaction diffusion competition model, Journal Dynam. Differential Equations, 22 (2010), 285-297. [CrossRef] [Google Scholar]
  20. W. Huang, M. Han, Non-linear determinacy of minimum wave speed for a Lotka-Volterra comptition model, J. Differential Euations, 251 (2011), 1549-1561. [CrossRef] [Google Scholar]
  21. V. Hutson, Y. Lou, K. Mischaikow, Spatial heterogeneity of resources versus Lotka-Volterra dynamics, J. Differential Equations, 185 (2002), 97–136. [CrossRef] [MathSciNet] [Google Scholar]
  22. V. Hutson, K. Mischaikow, P. Poláčik, The evolution of dispersal rates in a heterogeneous time-periodic environment, J. Math. Biol., 43 (2001) 501-533. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  23. V. Hutson, S. Martinez, K. Mischaikow, G.T. Vickers, The evolution of dispersal, J. Math. Biol., 47 (2003), 483-517. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  24. V. Hutson, W. Shen, G.T. Vickers, Spectral theory for nonlocal dispersal with periodic or almost-periodic time dependence, Rocky Mountain Journal of Mathematics, 38 (2008), 1147-1175. [CrossRef] [MathSciNet] [Google Scholar]
  25. C.-Y. Kao, Y. Lou, W. Shen, Random dispersal vs non-Local dispersal, Discrete and Continuous Dynamical Systems, 26 (2010), no. 2, 551-596. [MathSciNet] [Google Scholar]
  26. M. Lewis, B. Li, H. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Biol., 45 (2002), 219-233. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  27. B. Li, H. Weinberger, M. Lewis, Spreading speeds and slowest wave speeds for copperative systems, Math. Biosci., 196 (2005), 82-98. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  28. X. Liang, 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. [CrossRef] [MathSciNet] [Google Scholar]
  29. X. Liang, X.-Q. Zhao, Spreading speeds and traveling waves for abstract monostable evolution systems, Journal of Functional Analysis, 259 (2010), 857-903. [CrossRef] [MathSciNet] [Google Scholar]
  30. W.-T. Li, Y.-J. Sun, Z.-C. Wang, Entire solutions in the Fisher-KPP equation with nonlocal dispersal, Nonlinear Anal. Real World Appl., 11 (2010), 2302-2313. [CrossRef] [Google Scholar]
  31. R. Lui, Biological growth and spread modeled by systems of recursions, Math. Biosciences, 93 (1989), 269-312. [CrossRef] [Google Scholar]
  32. S. Pan, G. Lin, Invasion traveling wave solutions of a competitive system with dispersal, Boundary Value Problems, 2012:120. [Google Scholar]
  33. C. V. Pao, Coexistence and stability of a competition-diffusion system in population dynamics, J. Math. Anal. Appl., 83 (1981), 54-76. [CrossRef] [Google Scholar]
  34. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag New York Berlin Heidelberg Tokyo, 1983. [Google Scholar]
  35. Nar Rawal, W. Shen, Criteria for the existence and lower bounds of principal eigenvalues of time periodic nonlocal dispersal operators and applications, Journal of Dynamics and Differential Equations, 24 (2012), 927-954. [CrossRef] [MathSciNet] [Google Scholar]
  36. Nar Rawal, W. Shen, A. Zhang, Spreading speeds and traveling waves of nonlocal monostable equations in time and space periodic habitats, Discrete and Continuous Dynamical Systems, series A, 35 (2015), no. 4, 1609-1640. [CrossRef] [MathSciNet] [Google Scholar]
  37. W. Shen, A. Zhang, Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats, Journal of Differential Equations, 249 (2010), 747-795. [CrossRef] [Google Scholar]
  38. W. Shen, A. Zhang, Traveling wave solutions of monostable equations with nonlocal dispersal in space periodic habitats, Communications on Applied Nonlinear Analysis, 19 (2012), 73-101. [MathSciNet] [Google Scholar]
  39. W. Shen, A. Zhang, Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats, Proc. Amer. Math. Soc., 140 (2012), 1681-1696. [CrossRef] [MathSciNet] [Google Scholar]
  40. Hal L. Smith, Monotone Dynamical Systems, An Introduction to the Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs, 41. American Mathematical Society, Providence, RI, 1995. [Google Scholar]
  41. H. F. Weinberger, Long-time behavior of a class of biology models, SIAM J. Math. Anal., 13 (1982), 353-396. [CrossRef] [MathSciNet] [Google Scholar]
  42. H. F. Weinberger, On spreading speeds and traveling waves for growth and migration models in a periodic habitat, J. Math. Biol., 45 (2002), 511-548. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  43. H. Weinberger, M. Lewis, B. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol., 45 (2002), 183-218. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  44. X. Yu, X.-Q. Zhao, work in progress. [Google Scholar]
  45. X.-Q. Zhao, Dynamical Systems in Population Biology, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 16. Springer-Verlag, New York, 2003 [Google Scholar]
  46. L. Zhou, C. V. Pao, Asymptotic behavior of a competition-diffusion system in population dynamics, Nonlinear Anal., 6 (1982), 1163-1184. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.