Influence of Vibrations on Convective Instability of Reaction Fronts in Porous Media

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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.  
2. D. Aronson, H. Weinberger. Nonlinear Diffusion in Population Genetics, Combustion and Nerve Propagation. Lecture Notes in Math Vol. 446, pringer-Verlag, Berlin, 1975.  
3. B.S. Bhadauria, P.K. Bhatia L. Debnath. Convection in Hele-Shaw cell with parametric excitation. Int. Journal of Non-Linear Mechanics, 40 (2005), 475–484. 
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.  
5. N.F. Britton. Reaction-Diffusion Equations and Their Applications to Biology. Academic Press, New York, 1986.  
6. E. Brunet B. Derrida. Shift in the velocity of a front due to a cutoff. Phys. Rev. E, 56 (1997), 2597–2604. 
7. U. Ebert W. Van Saarloos. Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts. Physica D146 (2000), 1–99. 
8. M. Freidlin. Markov Processes and Differential Equations: Asymptotic Problems. Birkhauser, Basel, 1996.  
9. G.Z. Gershuni, A.K. Kolesnikov, J.C. Legros B.I. Myznikova. On the vibrational convective instability of a horizontal, binary-mixture layer with Soret effect. Journal of Fluid Mechanics, 330 (1997), 251–269. 
10. G.Z. Gershuni, E.M. Zhukhovitskii. The Convective Stability of Incompressible Fluids. Keter Publications, Jerusalem, (1976), 203–230.  
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.  
12. B.T. Murray, S.R. Coriell G.B. McFadden. The effect of gravity modulation on solutal convection during directional solidification. Journal of Crystal Growth, 110 (1991), 713–723. 
13. J.D. Murray. Mathematical Biology. Springer-Verlag, Berlin, 1989.  
14. A.C. Or. Finite-wavelength instability in a horizontal liquid layer on an oscillating plane. J. Fluid Mech., 335 (1997), 213–232. 
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.  
16. S. Rosenblat G.A. Tanaka. Modulation of thermal convection instability. Phys. Fluids, 7 (1971), 1319–1322. 
17. U.E. Volmar H.W. Muller. Quasiperiodic patterns in Rayleigh-Bénard convection under gravity modulation. Phys. Rev. E, 56 (1997), 5423–5430. 
18. V. Volpert S. Petrovskii. Reaction-diffusion waves in biology. Physics of Life Reviews, 6 (2009), 267–310. 
19. A. Volpert, Vit. Volpert, Vl. Volpert. Traveling wave solutions of parabolic system. American Mathematical Society, Providence, RI, (1994) 448 pp.  
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.  
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.  
22. G.H. Wolf. Dynamic stabilization of interchange instability of a liquid-gas interface. Phys. Rev. Lett., 24 (1970), 444–446. 
23. D.R. Woods S.P. Lin. Instability of a liquid film flow over a vibrating inclined plane. J. Fluid Mech., 294 (1995), 391–407. 
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.  
25. Ya.B. Zeldovich D.A. Frank-Kamenetsky. The theory of thermal propagation of flames. Zh. Fiz. Khim., 12 (1938), 100–105. 
26. S.M. Zenkovskaya. Action of high-frequency vibration on filtration convection. J. Appl. Mech. Tech. Phys., 32 (1992), 83–86. 
27. S.M. Zenkovskaya T.N. Rogovenko. Filtration convection in a high-frequency vibration field. J. Appl. Mech. Tech. Phys., 40 (1999), 379–385.