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Volumn 173, Issue 2, 2004, Pages 213-277

One-dimensional stability of viscous strong detonation waves

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EID: 4344568091     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00205-004-0317-6     Document Type: Article
Times cited : (28)

References (69)
  • 1
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability analysis of travelling waves
    • ALEXANDER, J., GARDNER, R., JONES, C.: A topological invariant arising in the stability analysis of travelling waves. J. Reine Agnew Math. 410, 167-212 (1990)
    • (1990) J. Reine Agnew Math. , vol.410 , pp. 167-212
    • Alexander, J.1    Gardner, R.2    Jones, C.3
  • 2
    • 0035538197 scopus 로고    scopus 로고
    • Alternate Evans functions and viscous shock waves
    • electronic
    • Benzoni-GAVAGE, S., SERRE, D., ZUMBRUN, K.: Alternate Evans functions and viscous shock waves. SIAM J. Math. Anal. 32, 929-962 (electronic) (2001)
    • (2001) SIAM J. Math. Anal. , vol.32 , pp. 929-962
    • Benzoni-Gavage, S.1    Serre, D.2    Zumbrun, K.3
  • 3
    • 0026142448 scopus 로고
    • Theoretical and numerical structure for unstable one-dimensional detonations
    • BURLIOUX, A., MAJDA, A.J., ROYTBURD, V.: Theoretical and numerical structure for unstable one-dimensional detonations. SIAM J. Appl. Math. 51, 303-343 (1991)
    • (1991) SIAM J. Appl. Math. , vol.51 , pp. 303-343
    • Burlioux, A.1    Majda, A.J.2    Roytburd, V.3
  • 4
    • 37049154758 scopus 로고
    • The Ignition of gases by an explosion wave, I:Carbon monoxide and carbon mixtures
    • CAMPBELL, C., WOODHEAD, D.W.: The Ignition of gases by an explosion wave, I:Carbon monoxide and carbon mixtures. J. Chem. Soc. 129, 3010-3021 (1926)
    • (1926) J. Chem. Soc. , vol.129 , pp. 3010-3021
    • Campbell, C.1    Woodhead, D.W.2
  • 5
    • 37049143174 scopus 로고
    • Striated photographic records of explosion waves
    • CAMPBELL, C., WOODHEAD, D.W.: Striated photographic records of explosion waves. J. Chem. Soc. 130, 1572-1578 (1927)
    • (1927) J. Chem. Soc. , vol.130 , pp. 1572-1578
    • Campbell, C.1    Woodhead, D.W.2
  • 9
    • 0001472248 scopus 로고
    • Nerve axon equations, I: Linear approximations
    • EVANS, J.: Nerve axon equations, I: Linear approximations. Indiana Univ. Math. J. 21, 877-855 (1972)
    • (1972) Indiana Univ. Math. J. , vol.21 , pp. 877-1855
    • Evans, J.1
  • 10
    • 0001472247 scopus 로고
    • Nerve axon equations, II: Stability at rest
    • EVANS, J.: Nerve axon equations, II: Stability at rest. Indiana Univ. Math. J. 22, 75-90 (1972)
    • (1972) Indiana Univ. Math. J. , vol.22 , pp. 75-90
    • Evans, J.1
  • 11
    • 0001472246 scopus 로고
    • Nerve axon equations, III: Stability of the nerve impulse
    • EVANS, J.: Nerve axon equations, III: Stability of the nerve impulse. Indiana Univ. Math. J. 22, 577-593 (1972)
    • (1972) Indiana Univ. Math. J. , vol.22 , pp. 577-593
    • Evans, J.1
  • 12
    • 0016578299 scopus 로고
    • Nerve axon equations, IV: The stable and unstable impulse
    • EVANS, J.: Nerve axon equations, IV: The stable and unstable impulse. Indiana Univ. Math. J. 24, 1169-1190 (1975)
    • (1975) Indiana Univ. Math. J. , vol.24 , pp. 1169-1190
    • Evans, J.1
  • 13
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • FENICHEL, N.: Geometric singular perturbation theory for ordinary differential equations. J. Differential Equations 31, 53-98 (1979)
    • (1979) J. Differential Equations , vol.31 , pp. 53-98
    • Fenichel, N.1
  • 15
    • 0000296180 scopus 로고
    • Flow calculations for pulsating one-dimensional detonations
    • FICKETT, W., WOOD, W.W.: Flow calculations for pulsating one-dimensional detonations. Phys. Fluids 9, 903-916 (1966)
    • (1966) Phys. Fluids , vol.9 , pp. 903-916
    • Fickett, W.1    Wood, W.W.2
  • 16
    • 0343208895 scopus 로고
    • Existence and bifurcation of viscous profiles for all intermediate magnetohydrodynamic shock waves
    • Freistühler, H., SZMOLYAN, P.: Existence and bifurcation of viscous profiles for all intermediate magnetohydrodynamic shock waves. SIAM J. Math. Anal. 26, 112-128 (1995)
    • (1995) SIAM J. Math. Anal. , vol.26 , pp. 112-128
    • Freistühler, H.1    Szmolyan, P.2
  • 17
    • 0040942605 scopus 로고    scopus 로고
    • The gap lemma and geometric criteria for the instability of viscous shocks
    • GARDNER, R., ZUMBRUN, K.: The gap lemma and geometric criteria for the instability of viscous shocks. Commun Pure Appl. Math. 51, 797-855 (1998)
    • (1998) Commun Pure Appl. Math. , vol.51 , pp. 797-855
    • Gardner, R.1    Zumbrun, K.2
  • 18
    • 21144479369 scopus 로고
    • A geometric singular perturbation analysis of detonation and deflagration waves
    • GASSER, I. SZMOLYAN, P.: A geometric singular perturbation analysis of detonation and deflagration waves. SIAM J. Math. Anal. 24, 968-986 (1993)
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 968-986
    • Gasser, I.1    Szmolyan, P.2
  • 19
    • 0000984677 scopus 로고
    • Detonation and deflagration waves with multistep reaction schemes
    • GASSER, I. SZMOLYAN, P.: Detonation and deflagration waves with multistep reaction schemes. SIAM J. Appl. Math. 55, 175-191 (1995)
    • (1995) SIAM J. Appl. Math. , vol.55 , pp. 175-191
    • Gasser, I.1    Szmolyan, P.2
  • 20
    • 0000247179 scopus 로고
    • Some problems in the theory of quasilinear equations
    • Gel'fand, I.M.: Some problems in the theory of quasilinear equations. Amer. Math. Soc. Transl. (2) 29, 295-381 (1963)
    • (1963) Amer. Math. Soc. Transl. (2) , vol.29 , pp. 295-381
    • Gel'fand, I.M.1
  • 21
    • 0000716762 scopus 로고
    • The existence and limit behavior of the one-dimensional shock layer
    • GILBARG, D.: The existence and limit behavior of the one-dimensional shock layer. Amer. J. Math. 73, 256-274 (1951)
    • (1951) Amer. J. Math. , vol.73 , pp. 256-274
    • Gilbarg, D.1
  • 24
    • 0012664789 scopus 로고    scopus 로고
    • Detonative travelling waves for combustions
    • HESAARAKI, M., RAZANI, A.: Detonative travelling waves for combustions. Applicable Anal. 77, 405-418 (2001)
    • (2001) Applicable Anal. , vol.77 , pp. 405-418
    • Hesaaraki, M.1    Razani, A.2
  • 27
    • 0002348145 scopus 로고    scopus 로고
    • Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations
    • KAPITULA, T., Sandstede B.: Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations. Phys. D 124, 58-103 (1998)
    • (1998) Phys. D , vol.124 , pp. 58-103
    • Kapitula, T.1    Sandstede, B.2
  • 28
    • 0037056338 scopus 로고    scopus 로고
    • Spinning instability of gaseous detonations
    • KASIMOV, A., STEWART, D.S.: Spinning instability of gaseous detonations. J. Fluid Mech. 466, 179-203 (2002)
    • (2002) J. Fluid Mech. , vol.466 , pp. 179-203
    • Kasimov, A.1    Stewart, D.S.2
  • 31
    • 0025461755 scopus 로고
    • Calculation of linear detonation instability: One-dimensional instability of plane detonation
    • LEE, H.I., STEWART, D.S.: Calculation of linear detonation instability: One-dimensional instability of plane detonation. J. Fluid Mech. 216, 103-132 (1990)
    • (1990) J. Fluid Mech. , vol.216 , pp. 103-132
    • Lee, H.I.1    Stewart, D.S.2
  • 32
    • 0030585881 scopus 로고    scopus 로고
    • Stability of strong detonation waves to combustion model
    • LI, D., LIU, T.-P., TAN, D.: Stability of strong detonation waves to combustion model. J. Math. Anal. Appl. 201, 516-531 (1996)
    • (1996) J. Math. Anal. Appl. , vol.201 , pp. 516-531
    • Li, D.1    Liu, T.-P.2    Tan, D.3
  • 33
    • 21144467405 scopus 로고
    • On the Riemann problem for a combustion model
    • LI, T.: On the Riemann problem for a combustion model. SIAM J. Math. Anal. 24, 59-75 (1993)
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 59-75
    • Li, T.1
  • 34
    • 0000138333 scopus 로고
    • On the initiation problem for a combustion model
    • LI, T.: On the initiation problem for a combustion model. J. Differential Equations 112, 351-373 (1994)
    • (1994) J. Differential Equations , vol.112 , pp. 351-373
    • Li, T.1
  • 35
    • 0000249989 scopus 로고    scopus 로고
    • Rigorous asymptotic stability of a Chapman-Jouget detonation wave in the limit of small resolved heat release
    • LI, T.: Rigorous asymptotic stability of a Chapman-Jouget detonation wave in the limit of small resolved heat release. Combustion Theory and Modeling 1, 259-270 (1997)
    • (1997) Combustion Theory and Modeling , vol.1 , pp. 259-270
    • Li, T.1
  • 36
    • 0002840914 scopus 로고    scopus 로고
    • Stability of strong detonation waves and rates of convergence
    • LI, T. : Stability of strong detonation waves and rates of convergence. Elec. J. Diff. Eqns. 1998, 1-77 (1998)
    • (1998) Elec. J. Diff. Eqns. , vol.1998 , pp. 1-77
    • Li, T.1
  • 38
    • 0041429241 scopus 로고
    • Nonlinear stability of strong detonations for a viscous combustion model
    • LIU, T.-R, YING, L.: Nonlinear stability of strong detonations for a viscous combustion model. SIAM J. Math. Analy. 26, 519-528 (1995)
    • (1995) SIAM J. Math. Analy. , vol.26 , pp. 519-528
    • Liu, T.-R.1    Ying, L.2
  • 39
    • 0033245368 scopus 로고    scopus 로고
    • Nonlinear stability of weak detonation waves for a combustion model
    • LIU, T.-P., YU, S.: Nonlinear stability of weak detonation waves for a combustion model. Commun. Math. Phys. 204, 551-586 (1999)
    • (1999) Commun. Math. Phys. , vol.204 , pp. 551-586
    • Liu, T.-P.1    Yu, S.2
  • 41
    • 4344596895 scopus 로고    scopus 로고
    • A stability index for detonation waves in majda's model for reacting flow
    • to appear
    • LYNG, G., ZUMBRUN, K.: A stability index for detonation waves in majda's model for reacting flow. Physica D, to appear
    • Physica D
    • Lyng, G.1    Zumbrun, K.2
  • 42
    • 0019599446 scopus 로고
    • A qualitative model for dynamic combustion
    • MAJDA, A.: A qualitative model for dynamic combustion. SIAM J. Appl. Math. 41, 70-93 (1981)
    • (1981) SIAM J. Appl. Math. , vol.41 , pp. 70-93
    • Majda, A.1
  • 44
    • 0002124586 scopus 로고
    • Stable viscosity matrices for systems of conservation laws
    • MAJDA, A., Pego R.L.: Stable viscosity matrices for systems of conservation laws. J. Differential Equations 56, 229-262 (1985)
    • (1985) J. Differential Equations , vol.56 , pp. 229-262
    • Majda, A.1    Pego, R.L.2
  • 46
    • 0013040387 scopus 로고    scopus 로고
    • Pointwise Green's function bounds and stability of relaxation shocks
    • MASCIA, C., ZUMBRUN, K.: Pointwise Green's function bounds and stability of relaxation shocks. Indiana Univ. Math. J. 51, 773-904 (2002)
    • (2002) Indiana Univ. Math. J. , vol.51 , pp. 773-904
    • Mascia, C.1    Zumbrun, K.2
  • 47
    • 0141957447 scopus 로고    scopus 로고
    • Pointwise Green function bounds for shock profiles of systems with real viscosity
    • MASCIA, C., ZUMBRUN, K.: Pointwise Green function bounds for shock profiles of systems with real viscosity. Arch. Ration. Mech. Anal. 169, 177-263 (2003)
    • (2003) Arch. Ration. Mech. Anal. , vol.169 , pp. 177-263
    • Mascia, C.1    Zumbrun, K.2
  • 48
    • 4344705452 scopus 로고    scopus 로고
    • Stability of viscous shock Profiles for dissipative symmetric hyperbolic-parabolic systems
    • to appear
    • MASCIA, C., ZUMBRUN, K.: Stability of viscous shock Profiles for dissipative symmetric hyperbolic-parabolic systems. Comm. Pure. Appl. Math., to appear
    • Comm. Pure. Appl. Math.
    • Mascia, C.1    Zumbrun, K.2
  • 49
    • 35949012093 scopus 로고    scopus 로고
    • The Riemann problem for fluid flow of real materials
    • MENIKOFF, R., PLOHR, B.J.: The Riemann problem for fluid flow of real materials. Rev. Modern Phys. 61, 75-130 (1999)
    • (1999) Rev. Modern Phys. , vol.61 , pp. 75-130
    • Menikoff, R.1    Plohr, B.J.2
  • 51
    • 0012726272 scopus 로고    scopus 로고
    • Stability of ZND detonation waves in the majda combustion model
    • ROQUEJOFFRE, J., Vila. J.: Stability of ZND detonation waves in the majda combustion model. Asymptotic Anal 18, 329-348 (1998)
    • (1998) Asymptotic Anal , vol.18 , pp. 329-348
    • Roquejoffre, J.1    Vila, J.2
  • 52
    • 23044528603 scopus 로고    scopus 로고
    • La transition vers l'instabilité pour les ondes de choc multi-dimensionnelles
    • electronic
    • SERRE, D.: La transition vers l'instabilité pour les ondes de choc multi-dimensionnelles. Trans. Amer. Math. Soc. 353, 5071-5093 (2001) (electronic)
    • (2001) Trans. Amer. Math. Soc. , vol.353 , pp. 5071-5093
    • Serre, D.1
  • 53
    • 0142008846 scopus 로고    scopus 로고
    • Boundary layer stability in real vanishing viscosity limit
    • SERRE, D., ZUMBRUN, K.: Boundary layer stability in real vanishing viscosity limit. Comm. Math. Phys. 202, 547-569 (2001)
    • (2001) Comm. Math. Phys. , vol.202 , pp. 547-569
    • Serre, D.1    Zumbrun, K.2
  • 54
    • 84972513592 scopus 로고
    • Systems of hyperbolic-parabolic type with applications to the discrete Boltzmann equation
    • SHIZUTA, Y., KAWASHIMA, S.: Systems of hyperbolic-parabolic type with applications to the discrete Boltzmann equation. Hokkaido Math. J. 14, 435-457 (1984)
    • (1984) Hokkaido Math. J. , vol.14 , pp. 435-457
    • Shizuta, Y.1    Kawashima, S.2
  • 55
    • 0031153871 scopus 로고    scopus 로고
    • Low-frequency two-dimensional linear instability of plane detonation
    • SHORT, M., STEWART, D.S.: Low-frequency two-dimensional linear instability of plane detonation. J. Fluid Mech. 340, 249-295 (1997)
    • (1997) J. Fluid Mech. , vol.340 , pp. 249-295
    • Short, M.1    Stewart, D.S.2
  • 56
    • 0032136260 scopus 로고    scopus 로고
    • Cellular detonation stability. I. A normal-mode linear analysis
    • SHORT, M., STEWART, D.S.: Cellular detonation stability. I. A normal-mode linear analysis. J. Fluid Mech. 368, 229-262 (1998)
    • (1998) J. Fluid Mech. , vol.368 , pp. 229-262
    • Short, M.1    Stewart, D.S.2
  • 57
    • 0032641555 scopus 로고    scopus 로고
    • The multi-dimensional stability of weak-heat-release detonations
    • SHORT, M., STEWART, D.S.: The multi-dimensional stability of weak-heat-release detonations. J. Fluid Mech. 382, 109-135 (1999)
    • (1999) J. Fluid Mech. , vol.382 , pp. 109-135
    • Short, M.1    Stewart, D.S.2
  • 58
    • 0033451346 scopus 로고    scopus 로고
    • Dynamics and stability of a weak detonation wave
    • SZEPESSY, A.: Dynamics and stability of a weak detonation wave. Commun. Math. Phys. 202, 547-569 (1999)
    • (1999) Commun. Math. Phys. , vol.202 , pp. 547-569
    • Szepessy, A.1
  • 59
    • 44949272344 scopus 로고
    • Transversal heteroclinic and homoclinic orbits in singular perturbation problems
    • SZMOLYAN, P.: Transversal heteroclinic and homoclinic orbits in singular perturbation problems. J. Differential Equations 92, 252-281 (1991)
    • (1991) J. Differential Equations , vol.92 , pp. 252-281
    • Szmolyan, P.1
  • 60
    • 0009047220 scopus 로고    scopus 로고
    • Nonlinear stability of strong detonation waves in gas dynamical combustion
    • TAN, D., TESEI, A.: Nonlinear stability of strong detonation waves in gas dynamical combustion. Nonlinearity 10, 355-376 (1997)
    • (1997) Nonlinearity , vol.10 , pp. 355-376
    • Tan, D.1    Tesei, A.2
  • 61
    • 84980080185 scopus 로고
    • Shock waves in arbitrary fluids
    • WEYL, H.: Shock waves in arbitrary fluids. Commun. Pure Appl. Math. 2, 103-122 (1949)
    • (1949) Commun. Pure Appl. Math. , vol.2 , pp. 103-122
    • Weyl, H.1
  • 64
    • 0347993642 scopus 로고    scopus 로고
    • Multidimensional stability of shock waves
    • Indiana University
    • ZUMBRUN, K.: Multidimensional stability of shock waves. Lecture Notes, Indiana University, 2000
    • (2000) Lecture Notes
    • Zumbrun, K.1
  • 65
    • 0001385446 scopus 로고    scopus 로고
    • Multidimensional stability of planar viscous shock waves
    • Progress in Nonlinear Differential Equations and Applications, Birkhauser
    • ZUMBRUN, K.: Multidimensional stability of planar viscous shock waves. In: Advances in the Theory of Shock Waves, number 47 in Progress in Nonlinear Differential Equations and Applications, pp. 307-516, Birkhauser, 2001
    • (2001) Advances in the Theory of Shock Waves , vol.47 , pp. 307-516
    • Zumbrun, K.1
  • 66
    • 0009378734 scopus 로고    scopus 로고
    • Pointwise semigroup methods and the stability of viscous shocks
    • ZUMBRUN, K., HOWARD, P.: Pointwise semigroup methods and the stability of viscous shocks. Indiana Univ. Math. J. 47, 741-871 (1998)
    • (1998) Indiana Univ. Math. J. , vol.47 , pp. 741-871
    • Zumbrun, K.1    Howard, P.2
  • 67
    • 0001028485 scopus 로고    scopus 로고
    • Viscous and inviscid stability of multidimensional planar shock fronts
    • ZUMBRUN, K., SERRE, D.: Viscous and inviscid stability of multidimensional planar shock fronts. Indiana Univ. Math. J. 48, 937-999 (1999)
    • (1999) Indiana Univ. Math. J. , vol.48 , pp. 937-999
    • Zumbrun, K.1    Serre, D.2
  • 69
    • 4344580679 scopus 로고    scopus 로고
    • Stability of large-amplitude shock waves of compressible Navier-Stokes Equations
    • Elsevier, to appear
    • ZUMBRUN, K.: Stability of Large-Amplitude shock waves of compressible Navier-Stokes Equations. Handbook Math. Fluid Dyn. IV Elsevier, to appear
    • Handbook Math. Fluid Dyn. IV
    • Zumbrun, K.1


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