Free Access
Editorial
Issue
Math. Model. Nat. Phenom.
Volume 10, Number 6, 2015
Nonlocal reaction-diffusion equations
Page(s) 1 - 5
DOI https://doi.org/10.1051/mmnp/201510601
Published online 02 October 2015
  1. M. Alfaro, J. Coville. Rapid travelling waves in the nonlocal Fisher equation connect two unstable states. Applied Mathematics Letters, 25 (2012), 2095-2099. [CrossRef]
  2. M. Alfaro, J. Coville, G. Raoul. Bistable travelling waves for nonlocal reaction diffusion equations. Discrete Contin. Dyn. Syst. Ser. A. 34 (2014), 1775–1791.
  3. S. Anita. Stabilization of a predator-prey system with nonlocal terms. Math. Model. Nat. Phenom., 10 (2015), no. 6, 6–16. [CrossRef] [EDP Sciences]
  4. N. Apreutesei, N. Bessonov, V. Volpert, V. Vougalter. Spatial structures and generalized travelling waves for an integro-differential equation. DCDS B, 13 (2010), No. 3, 537-557. [CrossRef]
  5. A. Apreutesei, A. Ducrot, V. Volpert. Competition of species with intra-specific competition. Math. Model. Nat. Phenom., 3 (2008), No. 4, 1-27. [CrossRef] [EDP Sciences] [MathSciNet]
  6. N. Apreutesei, A. Ducrot, V. Volpert. Travelling waves for integro-differential equations in population dynamics. DCDS B, 11 (2009), No. 3, 541-561. [CrossRef] [MathSciNet]
  7. N. Apreutesei, V. Volpert. Properness and topological degree for nonlocal reaction-diffusion operators. Abstract and Applied Analysis, 2011, Art. ID 629692, 21 pp.
  8. N. Apreutesei, V. Volpert. Properness and topological degree for nonlocal integro-differential systems. TMNA, 43 (2014), no. 1, 215-229.
  9. O. Aydogmus. Patterns and transitions to instability in an intraspecific competition model with nonlocal diffusion and interaction. Math. Model. Nat. Phenom., 10 (2015), no. 6, 17–29. [CrossRef] [EDP Sciences]
  10. A. Bayliss, V.A. Volpert. Patterns for competing populations with species specific nonlocal coupling. Math. Model. Nat. Phenom., 10 (2015), no. 6, 30–47. [CrossRef] [EDP Sciences]
  11. H. Berestycki, G. Nadin, B. Perthame, L. Ryzhik. The non-local Fisher-KPP equation: travelling waves and steady states. Nonlinearity, 22 (2009), no. 12, 2813–2844. [CrossRef]
  12. N. Bessonov, N. Reinberg, V. Volpert. Mathematics of Darwin’s diagram. Math. Model. Nat. Phenom., Vol. 9, No. 3, 2014, 5-25. [CrossRef] [EDP Sciences]
  13. N.F. Britton. Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model. SIAM J. Appl. Math., 6 (1990), 1663–1688. [CrossRef]
  14. J. Clairambault, P. Magal, V. Volpert. Cancer as evolutionary process. ESMTB Communcations, 2014, 17-20.
  15. I. Demin, V. Volpert. Existence of waves for a nonlocal reaction-diffusion equation. Math. Model. Nat. Phenom., 5 (2010), No. 5, 80-101. [CrossRef] [EDP Sciences]
  16. A. Ducrot, M. Marion, V. Volpert. Spectrum of some integro-differential operators and stability of travelling waves. Nonlinear Analysis Series A: Theory, Methods and Applications, 74 (2011), no. 13, 4455-4473. [CrossRef]
  17. M.A. Fuentes, M.O. Caceres. Stochastic path perturbation approach applied to nonlocal nonlinear equations in population dynamics. Math. Model. Nat. Phenom., 10 (2015), no. 6, 48–60. [CrossRef] [EDP Sciences]
  18. S. Genieys, N. Bessonov, V. Volpert. Mathematical model of evolutionary branching. Mathematical and computer modelling, 49 (2009), no. 11-12, 2109–2115. [CrossRef] [MathSciNet]
  19. S. Genieys, V. Volpert, P. Auger. Pattern and waves for a model in population dynamics with nonlocal consumption of resources. Mathem. Modelling of Natural Phenomena, 1, (2006), No. 1, 63-80. [CrossRef] [EDP Sciences]
  20. S. Genieys, V. Volpert, P. Auger. Adaptive dynamics: modelling Darwin’s divergence principle. Comptes Rendus Biologies, 329 (11), 876-879 (2006).
  21. S.A. Gourley. Travelling front solutions of a nonlocal Fisher equation, J. Math. Biol., 41 (2000), 272–284. [CrossRef] [MathSciNet] [PubMed]
  22. S.A. Gourley, M.A.J. Chaplain, F.A. Davidson. Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation. Dynamical systems, 16 (2001), no. 2, 173–192. [CrossRef] [MathSciNet]
  23. S.A. Gourley, R. Liu. An age-structured model of bird migration. Math. Model. Nat. Phenom., 10 (2015), no. 6, 61–76. [CrossRef] [EDP Sciences]
  24. I.J. Hewitt, A.A. Lacey, R. I. Todd. A mathematical model for flash sintering. Math. Model. Nat. Phenom., 10 (2015), no. 6, 77–89. [CrossRef] [EDP Sciences]
  25. N.I. Kavallaris, Y. Yan. A time discretization scheme for a nonlocal degenerate problem modelling resistance spot welding Math. Model. Nat. Phenom., 10 (2015), no. 6, 90–112. [CrossRef] [EDP Sciences]
  26. L. Kong, N. Rawal, W. Shen. Spreading speeds and linear determinacy for two species competition systems with nonlocal dispersal in periodic habitats. Math. Model. Nat. Phenom., 10 (2015), no. 6, 113–141. [CrossRef] [EDP Sciences]
  27. A. Lorz et al. Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies. Mathematical Modelling and Numerical Analysis, 47 (2013), 377-399.
  28. G. Nadin, L. Rossi, L. Ryzhik, B. Perthame. Wave-like solutions for nonlocal reaction-diffusion equations: a toy model. Math. Model. Nat.Phenom., 8 (2013), no. 3, 33–41. [CrossRef] [EDP Sciences] [MathSciNet]
  29. B. Perthame, S. Genieys. Concentration in the nonlocal Fisher equation: the Hamilton-Jacobi limit. Math. Model. Nat. Phenom., 4 (2007), 135–151. [CrossRef] [EDP Sciences]
  30. F. Thomas et al. Applying ecological and evolutionary theory to cancer: a long and winding road. Evol. Appl. 6 (2013), 1-10. [CrossRef] [PubMed]
  31. B.L. Segal, V.A. Volpert, A. Bayliss. Pattern formation in a model of competing populations with nonlocal interactions. Physica D, 253 (2013), 12-22. [CrossRef] [MathSciNet]
  32. S. Vakulenko, V. Volpert. Generalized travelling waves for perturbed monotone reaction-diffusion systems. Nonlinear Analysis. TMA, 2001 (46) 757-776. [CrossRef]
  33. V. Volpert. Elliptic partial differential equations. Volume 1. Fredholm theory of elliptic problems in unbounded domains. Birkhäuser, 2011.
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  35. V. Volpert. Branching and aggregation in self-reproducing systems. ESAIM: Proceedings and Surveys, 47 (2014), 116-129. [CrossRef] [EDP Sciences]
  36. V. Volpert. Pulses and waves for a bistable nonlocal reaction-diffusion equation. Applied Mathematics Letters, 44 (2015), 21-25. [CrossRef]
  37. V. Volpert, N. Reinberg, M. Benmir, S. Boujena. On pulse solutions of a reaction-diffusion system in population dynamics Nonlinear Analysis 120 (2015), 76-85. [CrossRef]
  38. V. Volpert, S. Petrovskii. Reaction-diffusion waves in biology. Physics of Life Reviews, 6 (2009), 267-310. [CrossRef] [PubMed]
  39. V. Volpert, V. Vougalter. Emergence and propagation of patterns in nonlocal reaction-diffusion equations arising in the theory of speciation. In: “Dispersal, individual movement and spatial ecology", Eds. M. Lewis, Ph. Maini, S. Petrovskii. Springer Applied Interdisciplinary Mathematics Series, in press.
  40. V. Vougalter, V. Volpert. Existence of stationary pulses for nonlocal reaction-diffusion equations, Documenta Mathematica, 19 (2014) 1141-1153. [MathSciNet]
  41. A. Volpert, Vit. Volpert, Vl. Volpert. Traveling wave solutions of parabolic systems. Translation of Mathematical Monographs, Vol. 140, Amer. Math. Society, Providence, 1994.
  42. G. Zhao, S. Ruan. The decay rates of traveling waves and spectral analysis for a class of nonlocal evolution equations. Math. Model. Nat. Phenom., 10 (2015), no. 6, 142–162. [CrossRef] [EDP Sciences]
  43. P. Zwolenski. Trait evolution in two-sex populations. Math. Model. Nat. Phenom., 10 (2015), no. 6, 163–181. [CrossRef] [EDP Sciences]

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