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All issues Volume 5 / No 5 (2010) Math. Model. Nat. Phenom., 5 5 (2010) 123-137 References
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Issue
Math. Model. Nat. Phenom.
Volume 5, Number 5, 2010
Reaction-diffusion waves
Page(s) 123 - 137
DOI https://doi.org/10.1051/mmnp/20105508
Published online 13 September 2010
  1. K. Allali, A. Ducrot, A. Taik, V. Volpert. Convective instability of reaction fronts in porous media. Math. Model. Nat. Phenom., 2 (2007), no. 2, 20–39. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  2. D. Aronson, H. Weinberger. Nonlinear Diffusion in Population Genetics, Combustion and Nerve Propagation. Lecture Notes in Math Vol. 446, pringer-Verlag, Berlin, 1975. [Google Scholar]
  3. B.S. Bhadauria, P.K. BhatiaL. Debnath. Convection in Hele-Shaw cell with parametric excitation. Int. Journal of Non-Linear Mechanics, 40 (2005), 475–484. [CrossRef] [Google Scholar]
  4. T. Boulal, S. Aniss, M. Belhaq, R. Rand. Effect of quasiperiodic gravitational modulation on the stability of a heated fluid layer. Phys. Rev. E. 52 (2007), 76, 56320. [Google Scholar]
  5. N.F. Britton. Reaction-Diffusion Equations and Their Applications to Biology. Academic Press, New York, 1986. [Google Scholar]
  6. E. BrunetB. Derrida. Shift in the velocity of a front due to a cutoff. Phys. Rev. E, 56 (1997), 2597–2604. [CrossRef] [MathSciNet] [Google Scholar]
  7. U. EbertW. Van Saarloos. Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts. Physica D 146 (2000), 1–99. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Freidlin. Markov Processes and Differential Equations: Asymptotic Problems. Birkhauser, Basel, 1996. [Google Scholar]
  9. G.Z. Gershuni, A.K. Kolesnikov, J.C. LegrosB.I. Myznikova. On the vibrational convective instability of a horizontal, binary-mixture layer with Soret effect. Journal of Fluid Mechanics, 330 (1997), 251–269. [Google Scholar]
  10. G.Z. Gershuni, E.M. Zhukhovitskii. The Convective Stability of Incompressible Fluids. Keter Publications, Jerusalem, (1976), 203–230. [Google Scholar]
  11. P.M. Gresho, R.L. Sani. The effects of gravity modulation on the stability of a heated fluid layer. J. Fluid Mech., 40 (1970), no. 4, 783–806. [Google Scholar]
  12. B.T. Murray, S.R. CoriellG.B. McFadden. The effect of gravity modulation on solutal convection during directional solidification. Journal of Crystal Growth, 110 (1991), 713–723. [CrossRef] [Google Scholar]
  13. J.D. Murray. Mathematical Biology. Springer-Verlag, Berlin, 1989. [Google Scholar]
  14. A.C. Or. Finite-wavelength instability in a horizontal liquid layer on an oscillating plane. J. Fluid Mech., 335 (1997), 213–232. [CrossRef] [MathSciNet] [Google Scholar]
  15. J.L. Rogers, M.F. Schatz, J.L. Bougie, J.B. Swift. Rayleigh-Bénard convection in a vertically oscillated fluid layer. Phys. Rev. Lett. 84 (2000), no. 1, 87–90. [CrossRef] [PubMed] [Google Scholar]
  16. S. RosenblatG.A. Tanaka. Modulation of thermal convection instability. Phys. Fluids, 7 (1971), 1319–1322. [Google Scholar]
  17. U.E. VolmarH.W. Muller. Quasiperiodic patterns in Rayleigh-Bénard convection under gravity modulation. Phys. Rev. E, 56 (1997), 5423–5430. [CrossRef] [Google Scholar]
  18. V. VolpertS. Petrovskii. Reaction-diffusion waves in biology. Physics of Life Reviews, 6 (2009), 267–310. [Google Scholar]
  19. A. Volpert, Vit. Volpert, Vl. Volpert. Traveling wave solutions of parabolic system. American Mathematical Society, Providence, RI, (1994) 448 pp. [Google Scholar]
  20. M. Wadih, B. Roux. The effects of gravity modulation on the stability of a heated fluid layer. J. Fluid Mech., 40 (1970), no. 4, 783–806. [Google Scholar]
  21. A.A. Wheeler, G.B. McFadden, B.T. Murray, S.R. Coriell. Convective stability in the Rayleigh-Bénard and directional solidification problems: high-frequency gravity modulation. Phys. Fluids A, 3 (1991), no. 12, 2847–2858. [CrossRef] [MathSciNet] [Google Scholar]
  22. G.H. Wolf. Dynamic stabilization of interchange instability of a liquid-gas interface. Phys. Rev. Lett., 24 (1970), 444–446. [CrossRef] [Google Scholar]
  23. D.R. WoodsS.P. Lin. Instability of a liquid film flow over a vibrating inclined plane. J. Fluid Mech., 294 (1995), 391–407. [CrossRef] [MathSciNet] [Google Scholar]
  24. Ya.B. Zeldovich, G.I. Barenblatt, V.B. Librovich, G.M. Makhviladze. The Mathematical Theory of Combustion and Explosions. Consultants Bureau, Plenum, New York, 1985. [Google Scholar]
  25. Ya.B. ZeldovichD.A. Frank-Kamenetsky. The theory of thermal propagation of flames. Zh. Fiz. Khim., 12 (1938), 100–105. [Google Scholar]
  26. S.M. Zenkovskaya. Action of high-frequency vibration on filtration convection. J. Appl. Mech. Tech. Phys., 32 (1992), 83–86. [Google Scholar]
  27. S.M. ZenkovskayaT.N. Rogovenko. Filtration convection in a high-frequency vibration field. J. Appl. Mech. Tech. Phys., 40 (1999), 379–385. [CrossRef] [Google Scholar]

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