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All issues Volume 10 / No 6 (2015) Math. Model. Nat. Phenom., 10 6 (2015) 1-5 References
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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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  7. N. Apreutesei, V. Volpert. Properness and topological degree for nonlocal reaction-diffusion operators. Abstract and Applied Analysis, 2011, Art. ID 629692, 21 pp. [Google Scholar]
  8. N. Apreutesei, V. Volpert. Properness and topological degree for nonlocal integro-differential systems. TMNA, 43 (2014), no. 1, 215-229. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  14. J. Clairambault, P. Magal, V. Volpert. Cancer as evolutionary process. ESMTB Communcations, 2014, 17-20. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  20. S. Genieys, V. Volpert, P. Auger. Adaptive dynamics: modelling Darwin’s divergence principle. Comptes Rendus Biologies, 329 (11), 876-879 (2006). [Google Scholar]
  21. S.A. Gourley. Travelling front solutions of a nonlocal Fisher equation, J. Math. Biol., 41 (2000), 272–284. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  27. A. Lorz et al. Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies. Mathematical Modelling and Numerical Analysis, 47 (2013), 377-399. [Google Scholar]
  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] [Google Scholar]
  29. B. Perthame, S. Genieys. Concentration in the nonlocal Fisher equation: the Hamilton-Jacobi limit. Math. Model. Nat. Phenom., 4 (2007), 135–151. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  32. S. Vakulenko, V. Volpert. Generalized travelling waves for perturbed monotone reaction-diffusion systems. Nonlinear Analysis. TMA, 2001 (46) 757-776. [CrossRef] [Google Scholar]
  33. V. Volpert. Elliptic partial differential equations. Volume 1. Fredholm theory of elliptic problems in unbounded domains. Birkhäuser, 2011. [Google Scholar]
  34. V. Volpert. Elliptic partial differential equations. Volume 2. Reaction-diffusion equations. Birkhäuser, 2014. [Google Scholar]
  35. V. Volpert. Branching and aggregation in self-reproducing systems. ESAIM: Proceedings and Surveys, 47 (2014), 116-129. [CrossRef] [EDP Sciences] [Google Scholar]
  36. V. Volpert. Pulses and waves for a bistable nonlocal reaction-diffusion equation. Applied Mathematics Letters, 44 (2015), 21-25. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  38. V. Volpert, S. Petrovskii. Reaction-diffusion waves in biology. Physics of Life Reviews, 6 (2009), 267-310. [Google Scholar]
  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. [Google Scholar]
  40. V. Vougalter, V. Volpert. Existence of stationary pulses for nonlocal reaction-diffusion equations, Documenta Mathematica, 19 (2014) 1141-1153. [MathSciNet] [Google Scholar]
  41. A. Volpert, Vit. Volpert, Vl. Volpert. Traveling wave solutions of parabolic systems. Translation of Mathematical Monographs, Vol. 140, Amer. Math. Society, Providence, 1994. [Google Scholar]
  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] [Google Scholar]
  43. P. Zwolenski. Trait evolution in two-sex populations. Math. Model. Nat. Phenom., 10 (2015), no. 6, 163–181. [CrossRef] [EDP Sciences] [Google Scholar]

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