Dynamics of a hyperbolic system that applies at the onset of the oscillatory instability

Nonlinearity

Volumn 11, Issue 1, 1998, Pages 105-142

  Martel, Carlos ^a   Vega, José M ^a  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011964664     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/11/1/008     Document Type: Article

References (30)

1. Courant R and Hilbert D 1962 Methods of Mathematical Physics vol II (New York: Interscience)
2. Coullet P, Fauve S and Tirapegui E 1985 Large scale instability of nonlinear standing waves J. Physique Lett. 46 787-91
3. Cross M C 1986 Travelling and standing waves in binary-fluid convection in finite geometries Phys. Rev. Lett. 57 2935-8
4. Martel C and Vega J M 1996 Finite size effects near the onset of the oscillatory instability Nonlinearity 9 1129-71
5. Cross M C and Hohenberg P C 1993 Pattern formation outside of equilibrium Rev. Mod. Phys. 65 851-1112
6. Chikwendu S C and Kevorkian J 1972 A perturbation method for hyperbolic equations with small nonlinearities SIAM J. Appl. Math. 22 235-58
7. Knobloch E and De Luca J 1990 Amplitude equations for travelling wave convection Nonlinearity 3 575-80
8. Alvarez-Pereira C and Vega J M 1992 On the pulsating instability of two-dimensional flames Eur. J. Appl. Math. 3 55-73
9. Vega J M 1993 On the amplitude equations arising at the onset of the oscillatory instability in pattern formation SIAM J. Math. Anal. 24 603-17
10. Duan J, van Ly H and Titi E S 1994/5 The effect of non-local interactions on the dynamics of the Ginzburg-Landau equation Institut Mittag-Leffer Tech. Report 31
11. Knobloch E and Gibbon J D 1991 Coupled NLS equations for counter propagating waves in systems with reflection symmetry Phys. Lett. A 154 353-6
12. Martel C 1995 La Inestabilidad Oscilatoria y sus Aplicaciones en Mecánica de Fluidos y Combustión Doctoral Thesis Univeridad Politécnica de Madrid, Madrid
13. Martel C and Vega J M 1997 A nonlocal amplitude equation that applies at the oscillatory instability in finite geometries, in preparation
14. Martel C and Vega J M 1997 Global stability properties of a hyperbolic system arising in pattern formation Nonlin. Anal. TMA 29 439-60
15. Tagg R, Edwards W S and Swinney H L 1990 Convective versus absolute instability in flow between counter-rotating cylinders Phys. Rev. A 42 831-7
16. Keller H B 1987 Lectures on Numerical Methods in Bifurcation Problems (Tata Institute of Fundamental Research, Bombay) (Berlin: Springer)
17. Wolf A, Swift J B, Swinney H L and Vastano J A 1985 Determining Lyapunov exponents from a time series Physica D 16 285-317
18. Croquette V and Williams H 1989 Nonlinear competition between waves on convective rolls Phys. Rev. A 39 2765-8
19. Croquette V and Williams H 1989 Nonlinear waves of the oscillatory instability on finite convective rolls Physica D 37 300-14
20. Clever R M and Busse F H 1974 Transition to time-dependent convection J. Fluid Mech. 65 625-45
21. Fauve S, Bolton E W and Brachet M E 1987 Nonlinear oscillatory convection: A quantitative phase dynamics approach Physica D 29 202-14
22. Preiser F, Schwabe D and Sharman A 1983 Steady an oscillatory thermocapillary convection in liquid columns with free cylindrical surfaces J. Fluid Mech. 126 545-67
23. Daviaud F and Vince J M 1993 Travelling waves in a fluid layer subjected to a horizontal temperature gradient Phys. Rev. E 48 4432-6
24. Vince J M and Dubois M 1992 Hot wire below the free surface of a liquid: Structural and dynamical properties of a secondary instability Europhys Lett. 20 505-10
25. Dubois M, Daviaud F, Rosin O and Bergé P 1992 Travelling waves in pure fluids locally heated along wires Physica D 61 140-6
26. Coullet P, Frisch T and Plaza F 1993 Sources and sinks in wave patterns Physica D 62 75-9
27. Andereck C D, Liu S S and Swinney H L 1986 Flow regimes in a circular Couette system with independently rotating cylinders J. Fluid Mech. 164 155-83
28. Predtechensky A A, McCormick W D, Swift J B, Noszticzius Z and Swinney H L 1994 Onset of travelling waves in isothermal double diffusive convection Phys. Rev. Lett. 72 218-21
29. Bensimon D, Kolodner P, Surko C M, Williams H and Croquette V 1990 Competing and coexisting dynamical states of travelling-wave convection in an annulus J. Fluid Mech. 217 441-67
30. Hohenberg P C, Kramer L and Riecke H 1985 Effects of boundaries on one-dimensional reaction-diffusion equations near threshold Physica D 15 402-20