Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 5, 2010
Reaction-diffusion waves
Page(s) 46 - 63
DOI https://doi.org/10.1051/mmnp/20105504
Published online 27 July 2010
  1. D. G. Aronson, H. F. Weinberger. Multidimensional diffusion arising in population genetics. Adv. Math., 30 (1978), 33–58. [NASA ADS] [CrossRef] [MathSciNet]
  2. H. L. Ashe, J. Briscoe. The interpretation of morphogen gradients. Development, 133 (2006), 385–394. [CrossRef] [PubMed]
  3. H. Berestycki, F. Hamel. Generalized travelling waves for reaction-diffusion equations. Perspectives in nonlinear partial differential equations, volume 446 of Contemp. Math., pages 101–123. Amer. Math. Soc., Providence, RI, 2007.
  4. J. D. Buckmaster, G. S. S. Ludford. Theory of laminar flames. Cambridge University Press, Cambridge, 1982.
  5. G. Chapuisat. Existence and nonexistence of curved front solution of a biological equation. J. Differential Equations 236 (2007), 237–279. [CrossRef] [MathSciNet]
  6. G. Chapuisat and R. Joly, Asymptotic profiles for a travelling front solution of a biological equation. Preprint.
  7. G. Dal Maso. An Introduction to Γ-Convergence. Birkhäuser, Boston, 1993.
  8. P. C. Fife.Mathematical Aspects of Reacting and Diffusing Systems. Springer-Verlag, Berlin, 1979.
  9. M. Freeman. Feedback control of intercellular signalling in development. Nature, 408 (2000), 313–319. [CrossRef] [PubMed]
  10. D. Gilbarg, N. S. Trudinger. Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin, 1983.
  11. U. Heberlin, K. Moses. Mechanisms of Drosophila retinal morphogenesis: the virtues of being progressive. Cell, 81 (1995), 987–990. [CrossRef] [PubMed]
  12. B. Kazmierczak, V. Volpert. Travelling calcium waves in systems with non-diffusing buffers. Math. Models Methods Appl. Sci., 18 (2008), 883–912. [CrossRef] [MathSciNet]
  13. J. Lembong, N. Yakoby, S. Y. Shvartsman. Pattern formation by dynamically interacting network motifs. Proc. Natl. Acad. Sci. USA, 106 (2009), 3213-3218. [CrossRef]
  14. M. Lucia, C. B. Muratov, M. Novaga. Existence of traveling waves of invasion for Ginzburg-Landau-type problems in infinite cylinders. Arch. Rational Mech. Anal., 188 (2008), 475–508. [CrossRef]
  15. A. Lunardi. Analytic semigroups and optimal regularity in parabolic problems, volume 16 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser, Basel, 1995.
  16. A. Martinez-Arias, A. Stewart. Molecular principles of animal development. Oxford University Press, New York, 2002.
  17. C. B. Muratov. A global variational structure and propagation of disturbances in reaction-diffusion systems of gradient type. Discrete Cont. Dyn. S., Ser. B, 4 (2004), 867–892. [CrossRef]
  18. C. B. Muratov, M. Novaga. Front propagation in infinite cylinders. I. A variational approach. Comm. Math. Sci., 6 (2008), 799–826.
  19. C. B. Muratov, F. Posta, S. Y. Shvartsman. Autocrine signal transmission with extracellular ligand degradation. Phys. Biol., 6 (2009), 016006. [CrossRef] [PubMed]
  20. C. B. Muratov, S. Y. Shvartsman. Signal propagation and failure in discrete autocrine relays. Phys. Rev. Lett., 93 (2004), 118101. [CrossRef] [PubMed]
  21. M. Přibyl, C. B. Muratov, S. Y. Shvartsman. Discrete models of autocrine cell communication in epithelial layers. Biophys. J., 84 (2003), 3624–3635. [CrossRef] [PubMed]
  22. M. Přibyl, C. B. Muratov, S. Y. Shvartsman. Long-range signal transmission in autocrine relays. Biophys. J., 84 (2003), 883–896. [CrossRef] [PubMed]
  23. N. Shigesada, K. Kawasaki. Biological invasions: theory and practice. Oxford Series in Ecology and Evolution. Oxford Univ. Press, Oxford, 1997.
  24. T. Tabata, Y. Takei. Morphogens, their identification and regulation. Development, 131 (2004), 703–712. [CrossRef] [PubMed]
  25. J. J. Tyson, K. Chen, B. Novak. Network dynamics and cell physiology. Nat. Rev. Mol. Cell Biol., 2 (2001), 908–916. [CrossRef] [PubMed]
  26. A. I. Volpert, V. A. Volpert, V. A. Volpert. Traveling wave solutions of parabolic systems. AMS, Providence, 1994.
  27. V. Volpert, A. Volpert. Existence of multidimensional travelling waves in the bistable case. C. R. Acad. Sci. Paris Sér. I Math., 328 (1999), 245–250.
  28. H. S. Wiley, S. Y. Shvartsman, D. A. Lauffenburger. Computational modeling of the EGF-receptor system: a paradigm for systems biology. Trends Cell Biol., 13 (2003), 43–50. [CrossRef] [PubMed]
  29. L. Wolpert, R. Beddington, T. Jessel, P. Lawrence, E. Meyerowitz. Principles of Development. Oxford University Press, Oxford, 1998.
  30. J. Xin. Front propagation in heterogeneous media. SIAM Review, 42 (2000), 161–230. [CrossRef] [MathSciNet]
  31. N. Yakoby, J. Lembong, T. Schüpbach, S. Y. Shvartsman Drosophila eggshell is patterned by sequential action of feedforward and feedback loops. Development, 135 (2008), 343–351. [CrossRef] [PubMed]

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.