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Volumn 67, Issue 2, 2006, Pages 464-486

High Lewis number combustion wavefronts: A perturbative Melnikov analysis

Author keywords

Combustion waves; Evans function; High Lewis number; Melnikov's method; Slow manifold reduction

Indexed keywords

COMBUSTION WAVES; EVANS FUNCTION; LEWIS NUMBER; MELNIKOV'S METHOD; SLOW MANIFOLD REDUCTION;

EID: 34247577468     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/050640849     Document Type: Article
Times cited : (21)

References (40)
  • 1
    • 0043257701 scopus 로고    scopus 로고
    • Instability of the Hocking-Stewartson pulse and its implications for the three-dimensional Poiseuille flow
    • A. L. AFENDIKOV AND T. J. BRIDGES, Instability of the Hocking-Stewartson pulse and its implications for the three-dimensional Poiseuille flow, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 457 (2001), pp. 257-272.
    • (2001) R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci , vol.457 , pp. 257-272
    • AFENDIKOV, A.L.1    BRIDGES, T.J.2
  • 2
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability analysis of travelling waves
    • J. ALEXANDER, R. GARDNER, AND C. JONES, A topological invariant arising in the stability analysis of travelling waves, J. Reine Angew. Math., 410 (1990), pp. 167-212.
    • (1990) J. Reine Angew. Math , vol.410 , pp. 167-212
    • ALEXANDER, J.1    GARDNER, R.2    JONES, C.3
  • 3
    • 0035982252 scopus 로고    scopus 로고
    • Numerical exterior algebra and the compound matrix method
    • L. ALLEN AND T. J. BRIDGES, Numerical exterior algebra and the compound matrix method, Numer. Math., 92 (2002), pp. 197-232.
    • (2002) Numer. Math , vol.92 , pp. 197-232
    • ALLEN, L.1    BRIDGES, T.J.2
  • 5
    • 0025413863 scopus 로고
    • Two routes to chaos in condensed phase combustion
    • A. BAYLISS AND B. J. MATKOWSKY, Two routes to chaos in condensed phase combustion, SIAM J. Appl. Math., 50 (1990), pp. 437-459.
    • (1990) SIAM J. Appl. Math , vol.50 , pp. 437-459
    • BAYLISS, A.1    MATKOWSKY, B.J.2
  • 6
    • 0028369845 scopus 로고
    • From traveling waves to chaos in combustion
    • A. BAYLISS AND B. J. MATKOWSKY, From traveling waves to chaos in combustion, SIAM J. Appl. Math., 54 (1994), pp. 147-174.
    • (1994) SIAM J. Appl. Math , vol.54 , pp. 147-174
    • BAYLISS, A.1    MATKOWSKY, B.J.2
  • 7
    • 0347997366 scopus 로고    scopus 로고
    • Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms
    • J. BILLINGHAM, Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms, Dyn. Stab. Syst., 15 (2000), pp. 23-33.
    • (2000) Dyn. Stab. Syst , vol.15 , pp. 23-33
    • BILLINGHAM, J.1
  • 8
    • 0034773810 scopus 로고    scopus 로고
    • The effect of heat loss on the propagation of strongly exothermic combustion waves
    • J. BILLINGHAM AND G. N. MERCER, The effect of heat loss on the propagation of strongly exothermic combustion waves, Combust. Theory Model., 5 (2001), pp. 319-342.
    • (2001) Combust. Theory Model , vol.5 , pp. 319-342
    • BILLINGHAM, J.1    MERCER, G.N.2
  • 10
    • 0000382917 scopus 로고    scopus 로고
    • Hodge duality and the Evans function
    • T. J. BRIDGES AND G. DERKS, Hodge duality and the Evans function, Phys. Lett. A, 251 (1999), pp. 363-372.
    • (1999) Phys. Lett. A , vol.251 , pp. 363-372
    • BRIDGES, T.J.1    DERKS, G.2
  • 11
    • 0037112236 scopus 로고    scopus 로고
    • Stability and instability of solitary waves of the fifth-order KdV equation: A numerical framework
    • T. J. BRIDGES, G. DERKS, AND G. GOTTWALD, Stability and instability of solitary waves of the fifth-order KdV equation: A numerical framework, Phys. D, 172 (2002), pp. 190-216.
    • (2002) Phys. D , vol.172 , pp. 190-216
    • BRIDGES, T.J.1    DERKS, G.2    GOTTWALD, G.3
  • 12
    • 0035646092 scopus 로고    scopus 로고
    • Numerical testing of the stability of viscous shock waves
    • L. Q. BRIN, Numerical testing of the stability of viscous shock waves, Math. Comp., 70 (2001), pp. 1071-1088.
    • (2001) Math. Comp , vol.70 , pp. 1071-1088
    • BRIN, L.Q.1
  • 13
    • 0000670035 scopus 로고
    • Asymptotic analysis of laminar flame propagation for general Lewis numbers
    • W. BUSH AND F. FENDELL, Asymptotic analysis of laminar flame propagation for general Lewis numbers, Combust. Sci. Tech., 1 (1970), pp. 421-428.
    • (1970) Combust. Sci. Tech , vol.1 , pp. 421-428
    • BUSH, W.1    FENDELL, F.2
  • 14
    • 20444459129 scopus 로고    scopus 로고
    • A numerical study of one-step models of polymerization: Frontal versus bulk mode
    • S. A. CARDARELLI, D. GOLOVATY, L. K. GROSS, V. T. GYRYA, AND J. ZHU, A numerical study of one-step models of polymerization: Frontal versus bulk mode, Phys. D, 206 (2005), pp. 145-165.
    • (2005) Phys. D , vol.206 , pp. 145-165
    • CARDARELLI, S.A.1    GOLOVATY, D.2    GROSS, L.K.3    GYRYA, V.T.4    ZHU, J.5
  • 15
    • 33644882810 scopus 로고    scopus 로고
    • A robust numerical method to study oscillatory instability of gap solitary waves
    • G. DERKS AND G. A. GOTTWALD, A robust numerical method to study oscillatory instability of gap solitary waves, SIAM J. Appl. Dyn. Syst., 4 (2005), pp. 140-158.
    • (2005) SIAM J. Appl. Dyn. Syst , vol.4 , pp. 140-158
    • DERKS, G.1    GOTTWALD, G.A.2
  • 16
    • 0016578299 scopus 로고
    • Nerve axon equations. IV. The stable and the unstable impulse
    • J. W. EVANS, Nerve axon equations. IV. The stable and the unstable impulse, Indiana Univ. Math. J., 24 (1974/75), pp. 1169-1190.
    • (1974) Indiana Univ. Math. J , vol.24 , pp. 1169-1190
    • EVANS, J.W.1
  • 17
    • 0017565869 scopus 로고
    • Local stability theory of the nerve impulse
    • J. W. EVANS AND N. FEROE, Local stability theory of the nerve impulse, Math. Biosci., 37 (1977), pp. 23-50.
    • (1977) Math. Biosci , vol.37 , pp. 23-50
    • EVANS, J.W.1    FEROE, N.2
  • 18
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • N. FENICHEL, Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J., 21 (1971), pp. 193-226.
    • (1971) Indiana Univ. Math. J , vol.21 , pp. 193-226
    • FENICHEL, N.1
  • 22
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer-Verlag, Berlin
    • D. HENRY, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math. 840, Springer-Verlag, Berlin, 1981.
    • (1981) Lecture Notes in Math , vol.840
    • HENRY, D.1
  • 23
    • 84967743294 scopus 로고
    • Stability of the travelling wave solution of the FitzHugh-Nagumo system
    • C.K. R. T. JONES, Stability of the travelling wave solution of the FitzHugh-Nagumo system, Trans. Amer. Math. Soc., 286 (1984), pp. 431-469.
    • (1984) Trans. Amer. Math. Soc , vol.286 , pp. 431-469
    • JONES, C.K.R.T.1
  • 25
    • 0000908821 scopus 로고
    • Multiplicity and stability of supercritical combustion in a nonadiabatic tubular reactor
    • S. MARGOLIS AND S. JOHNSTON, Multiplicity and stability of supercritical combustion in a nonadiabatic tubular reactor, Combust. Sci. Tech., 65 (1989), pp. 103-136.
    • (1989) Combust. Sci. Tech , vol.65 , pp. 103-136
    • MARGOLIS, S.1    JOHNSTON, S.2
  • 26
    • 0001603791 scopus 로고
    • Diffusion/thermal instability of solid propellant flame
    • S. B. MARGOLIS AND F. A. WILLIAMS, Diffusion/thermal instability of solid propellant flame, SIAM J. Appl. Math., 49 (1989), pp. 1390-1420.
    • (1989) SIAM J. Appl. Math , vol.49 , pp. 1390-1420
    • MARGOLIS, S.B.1    WILLIAMS, F.A.2
  • 27
    • 0025910686 scopus 로고
    • Flame propagation in solids and high-density fluids with Arrhenius reactant diffusion
    • S. B. MARGOLIS AND F. A. WILLIAMS, Flame propagation in solids and high-density fluids with Arrhenius reactant diffusion, Comb. Flame, 83 (1991), pp. 390-398.
    • (1991) Comb. Flame , vol.83 , pp. 390-398
    • MARGOLIS, S.B.1    WILLIAMS, F.A.2
  • 28
    • 0018031317 scopus 로고
    • Propagation of a pulsating reaction front in solid fuel combustion
    • B. J. MATKOWSKY AND G. I. SIVASHINSKY, Propagation of a pulsating reaction front in solid fuel combustion, SIAM J. Appl. Math., 35 (1978), pp. 465-478.
    • (1978) SIAM J. Appl. Math , vol.35 , pp. 465-478
    • MATKOWSKY, B.J.1    SIVASHINSKY, G.I.2
  • 29
    • 0001834849 scopus 로고
    • On the stability of the centre for time-periodic perturbations
    • V. K. MELNIKOV, On the stability of the centre for time-periodic perturbations, Trans. Moscow Math. Soc., 12 (1963), pp. 1-56.
    • (1963) Trans. Moscow Math. Soc , vol.12 , pp. 1-56
    • MELNIKOV, V.K.1
  • 30
    • 0030775004 scopus 로고    scopus 로고
    • Combustion waves in two dimensions and their one-dimensional approximation
    • G. N. MERCER AND R. O. WEBER, Combustion waves in two dimensions and their one-dimensional approximation, Combust. Theory Model., 1 (1997), pp. 157-165.
    • (1997) Combust. Theory Model , vol.1 , pp. 157-165
    • MERCER, G.N.1    WEBER, R.O.2
  • 31
    • 0001640902 scopus 로고
    • An initial-value method for eigenvalue problems using compound matrices, 3
    • B. NG AND W. REID, An initial-value method for eigenvalue problems using compound matrices, 3. Comput. Phys., 30 (1979), pp. 125-136.
    • (1979) Comput. Phys , vol.30 , pp. 125-136
    • NG, B.1    REID, W.2
  • 32
    • 0001726136 scopus 로고
    • Oscillatory instability of solitary waves in a continuum model of lattice vibrations
    • R. L. PEGO, P. SMERAKA, AND M.I. WEINSTEIN, Oscillatory instability of solitary waves in a continuum model of lattice vibrations, Nonlinearity, 8 (1995), pp. 92-941.
    • (1995) Nonlinearity , vol.8 , pp. 92-941
    • PEGO, R.L.1    SMERAKA, P.2    WEINSTEIN, M.I.3
  • 34
    • 0142218519 scopus 로고    scopus 로고
    • Evans function analysis of the stability of non-adiabatic flames
    • P. SIMON, S. KALLIADASIS, J. MERKIN, AND S. SCOTT, Evans function analysis of the stability of non-adiabatic flames, Combust. Theory Model., 7 (2003), pp. 545-561.
    • (2003) Combust. Theory Model , vol.7 , pp. 545-561
    • SIMON, P.1    KALLIADASIS, S.2    MERKIN, J.3    SCOTT, S.4
  • 35
    • 0000470794 scopus 로고
    • Stability of travelling pulse to a laser equation
    • J. SWINTON AND J. ELGIN, Stability of travelling pulse to a laser equation, Phys. Lett. A, 145 (1990), pp. 428-433.
    • (1990) Phys. Lett. A , vol.145 , pp. 428-433
    • SWINTON, J.1    ELGIN, J.2
  • 36
    • 0036588787 scopus 로고    scopus 로고
    • Linear stability of a plane front in solid combustion at large heat of reaction
    • F. VARAS AND J. M. VEGA, Linear stability of a plane front in solid combustion at large heat of reaction, SIAM J. Appl. Math., 62 (2002), pp. 1810-1822.
    • (2002) SIAM J. Appl. Math , vol.62 , pp. 1810-1822
    • VARAS, F.1    VEGA, J.M.2
  • 39
    • 0034206088 scopus 로고    scopus 로고
    • Front propagation in heterogeneous media
    • J. XIN, Front propagation in heterogeneous media, SIAM Rev., 42 (2000), pp. 161-230.
    • (2000) SIAM Rev , vol.42 , pp. 161-230
    • XIN, J.1
  • 40
    • 0021853023 scopus 로고
    • Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations
    • E. YANAGIDA, Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations, J. Math. Biol., 22 (1985), pp. 81-104.
    • (1985) J. Math. Biol , vol.22 , pp. 81-104
    • YANAGIDA, E.1


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