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All issues Volume 5 / No 5 (2010) Math. Model. Nat. Phenom., 5 5 (2010) 46-63 References
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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. [Google Scholar]
  2. H. L. Ashe, J. Briscoe. The interpretation of morphogen gradients. Development, 133 (2006), 385–394. [CrossRef] [PubMed] [Google Scholar]
  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. [Google Scholar]
  4. J. D. Buckmaster, G. S. S. Ludford. Theory of laminar flames. Cambridge University Press, Cambridge, 1982. [Google Scholar]
  5. G. Chapuisat. Existence and nonexistence of curved front solution of a biological equation. J. Differential Equations 236 (2007), 237–279. [CrossRef] [MathSciNet] [Google Scholar]
  6. G. Chapuisat and R. Joly, Asymptotic profiles for a travelling front solution of a biological equation. Preprint. [Google Scholar]
  7. G. Dal Maso. An Introduction to Γ-Convergence. Birkhäuser, Boston, 1993. [Google Scholar]
  8. P. C. Fife.Mathematical Aspects of Reacting and Diffusing Systems. Springer-Verlag, Berlin, 1979. [Google Scholar]
  9. M. Freeman. Feedback control of intercellular signalling in development. Nature, 408 (2000), 313–319. [CrossRef] [PubMed] [Google Scholar]
  10. D. Gilbarg, N. S. Trudinger. Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin, 1983. [Google Scholar]
  11. U. Heberlin, K. Moses. Mechanisms of Drosophila retinal morphogenesis: the virtues of being progressive. Cell, 81 (1995), 987–990. [CrossRef] [PubMed] [Google Scholar]
  12. B. Kazmierczak, V. Volpert. Travelling calcium waves in systems with non-diffusing buffers. Math. Models Methods Appl. Sci., 18 (2008), 883–912. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  16. A. Martinez-Arias, A. Stewart. Molecular principles of animal development. Oxford University Press, New York, 2002. [Google Scholar]
  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] [Google Scholar]
  18. C. B. Muratov, M. Novaga. Front propagation in infinite cylinders. I. A variational approach. Comm. Math. Sci., 6 (2008), 799–826. [Google Scholar]
  19. C. B. Muratov, F. Posta, S. Y. Shvartsman. Autocrine signal transmission with extracellular ligand degradation. Phys. Biol., 6 (2009), 016006. [CrossRef] [PubMed] [Google Scholar]
  20. C. B. Muratov, S. Y. Shvartsman. Signal propagation and failure in discrete autocrine relays. Phys. Rev. Lett., 93 (2004), 118101. [CrossRef] [PubMed] [Google Scholar]
  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] [Google Scholar]
  22. M. Přibyl, C. B. Muratov, S. Y. Shvartsman. Long-range signal transmission in autocrine relays. Biophys. J., 84 (2003), 883–896. [CrossRef] [PubMed] [Google Scholar]
  23. N. Shigesada, K. Kawasaki. Biological invasions: theory and practice. Oxford Series in Ecology and Evolution. Oxford Univ. Press, Oxford, 1997. [Google Scholar]
  24. T. Tabata, Y. Takei. Morphogens, their identification and regulation. Development, 131 (2004), 703–712. [CrossRef] [PubMed] [Google Scholar]
  25. J. J. Tyson, K. Chen, B. Novak. Network dynamics and cell physiology. Nat. Rev. Mol. Cell Biol., 2 (2001), 908–916. [Google Scholar]
  26. A. I. Volpert, V. A. Volpert, V. A. Volpert. Traveling wave solutions of parabolic systems. AMS, Providence, 1994. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  29. L. Wolpert, R. Beddington, T. Jessel, P. Lawrence, E. Meyerowitz. Principles of Development. Oxford University Press, Oxford, 1998. [Google Scholar]
  30. J. Xin. Front propagation in heterogeneous media. SIAM Review, 42 (2000), 161–230. [CrossRef] [MathSciNet] [Google Scholar]
  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] [Google Scholar]

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