Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 5, 2010
Reaction-diffusion waves
Page(s) 80 - 101
DOI https://doi.org/10.1051/mmnp/20105506
Published online 27 July 2010
  1. S. Ai. Traveling wave fronts for generalized Fisher equations with spatio-temporal delays. J. Differential Equations, 232 (2007), 104–133. [CrossRef] [MathSciNet]
  2. A. Apreutesei, A. Ducrot, V. Volpert. Competition of species with intra-specific competition. Math. Model. Nat. Phenom., 3 (2008), 1–27. [CrossRef] [EDP Sciences] [MathSciNet]
  3. N. Apreutesei, A. Ducrot, V. Volpert. Travelling waves for integro-differential equations in population dynamics. Discrete Cont. Dyn. Syst. Ser. B, 11 (2009), 541–561. [CrossRef] [MathSciNet]
  4. 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]
  5. A. Ducrot, Travelling wave solutions for a scalar age-structured equation, Discrete Contin. Dyn. Syst. Ser. B , 7 (2007), 251–273. [CrossRef] [MathSciNet]
  6. P. C. Fife, J. B. McLeod. The approach of solutions of nonlinear diffusion equations to travelling wave solutions. Bull. Amer. Math. Soc., 81 (1975), 1076–1078. [CrossRef] [MathSciNet]
  7. A. Friedman. Partial differential equations of parabolic type. Prentice-Hall, Englewood Cliffs, 1964.
  8. S. Génieys, V. Volpert, P. Auger. Pattern and waves for a model in population dynamics with nonlocal consumption of resources. Math. Model. Nat. Phenom., 1 (2006), 63–80. [CrossRef] [EDP Sciences]
  9. S. A. Gourley. Travelling front solutions of a nonlocal Fisher equation. J. Math. Biol. 41 (2000), 272–284. [CrossRef] [MathSciNet] [PubMed]
  10. Ya. I. Kanel. The behavior of solutions of the Cauchy problem when the time tends to infinity, in the case of quasilinear equations arising in the theory of combustion. Soviet Math. Dokl. 1 (1960), 533–536.
  11. R. Lefever, O. Lejeune. On the origin of tiger bush. Bul. Math. Biol., 59 (1997), No. 2, 263–294. [CrossRef]
  12. A.I. Volpert, V.A. Volpert. Applications of the rotation theory of vector fields to the study of wave solutions of parabolic equations. Trans. Moscow Math. Soc., 52 (1990), 59–108.
  13. A. Volpert, Vl. Volpert, Vit. Volpert. Travelling wave solutions of parabolic systems. 1994, AMS, Providence.
  14. V. Volpert, A. Volpert, J.F. Collet. Topological degree for elliptic operators in unbounded cylinders. Adv. Diff. Eq., 4 (1999), 777–812.
  15. V. Volpert, A. Volpert. Properness and topological degree for general elliptic operators. Abstract and Applied Analysis, 2003 (2003), 129–181. [CrossRef]
  16. A. Volpert, V. Volpert. Normal solvability of general linear elliptic problems. Abstract and Applied Analysis, 7 (2005), 733–756. [CrossRef]
  17. Y. Wang, J. Yin, Travelling waves for a biological reaction diffusion model with spatio- temporal delay, J. Math. Anal. Appl., 325 (2007), 1400–1409. [CrossRef] [MathSciNet]
  18. Z.C. Wang, W.T. Li, S. Ruan, Travelling wave fronts in reaction-diffusion systems with spatio-temporal delays, J. Diff. Equations, 222 (2006), 185–232. [CrossRef]

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.