메뉴 건너뛰기




Volumn 134, Issue 4, 1996, Pages 341-402

Bifurcations of travelling waves in the thermo-diffusive model for flame propagation

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0002047642     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00375113     Document Type: Article
Times cited : (10)

References (38)
  • 1
    • 84980079270 scopus 로고
    • Properties of solutions of ordinary differential equations in Banach space
    • S. AGMON & L. NIRENBERG, Properties of solutions of ordinary differential equations in Banach space, Comm. Pure Appl. Math., 16 (1963), 121-239.
    • (1963) Comm. Pure Appl. Math. , vol.16 , pp. 121-239
    • Agmon, S.1    Nirenberg, L.2
  • 2
    • 0005235678 scopus 로고
    • A topological invariant arising in the stability analysis of travelling waves
    • J. ALEXANDER, R. GARDNER & C. K. R. T. JONES, A topological invariant arising in the stability analysis of travelling waves, J. reine angew. Math., 410 (1990), 167-212.
    • (1990) J. Reine Angew. Math. , vol.410 , pp. 167-212
    • Alexander, J.1    Gardner, R.2    Jones, C.K.R.T.3
  • 3
    • 0038910708 scopus 로고
    • On the dirichlet problem for infinite cylinders and equations with transversely, varying coefficients
    • C. J. AMICK, On the Dirichlet problem for infinite cylinders and equations with transversely, varying coefficients, J. Diff. Eq., 30 (1978), 248-279.
    • (1978) J. Diff. Eq. , vol.30 , pp. 248-279
    • Amick, C.J.1
  • 5
    • 0024770387 scopus 로고
    • A finite element adaptative investigation of curved stable and unstable flame front
    • F. BENKHALDOUN & B. LARROUTUROU, A finite element adaptative investigation of curved stable and unstable flame front, Comp. Meth. in Appl. Science and Eng., 76 (1989), 119-134.
    • (1989) Comp. Meth. in Appl. Science and Eng. , vol.76 , pp. 119-134
    • Benkhaldoun, F.1    Larrouturou, B.2
  • 6
    • 0002195388 scopus 로고
    • Quelques aspects mathématiques de la propagation des flammes prëmélangées
    • Collège de France Seminar, BREZIS & LIONS, eds. Pitman Longman, Harlow (U.K.)
    • H. BERESTYCKI & B. LARROUTUROU, Quelques aspects mathématiques de la propagation des flammes prëmélangées, Nonlinear partial differential equations and their applications, Collège de France Seminar, 10, BREZIS & LIONS, eds. Pitman Longman, Harlow (U.K.), 1990.
    • (1990) Nonlinear Partial Differential Equations and Their Applications , vol.10
    • Berestycki, H.1    Larrouturou, B.2
  • 7
    • 0002626724 scopus 로고
    • Multidimensional travelling wave solutions of a flame propagation model
    • H. BERESTYCKI, B. LARROUTUROU & P.-L. LIONS, Multidimensional travelling wave solutions of a flame propagation model, Arch. Rational Mech. Anal., 111 (1990), 33-49.
    • (1990) Arch. Rational Mech. Anal. , vol.111 , pp. 33-49
    • Berestycki, H.1    Larrouturou, B.2    Lions, P.-L.3
  • 9
    • 0002785224 scopus 로고
    • Stability of travelling fronts in a model for flame propagation. Part I: Linear analysis
    • H. BERESTYCKI, B. LARROUTUROU & J.-M. ROQUEJOFFRE, Stability of travelling fronts in a model for flame propagation. Part I: Linear analysis. Arch. Rational Mech. Anal., 117 (1992), 97-117.
    • (1992) Arch. Rational Mech. Anal. , vol.117 , pp. 97-117
    • Berestycki, H.1    Larrouturou, B.2    Roquejoffre, J.-M.3
  • 10
    • 0000469757 scopus 로고
    • Traveling wave solutions to combustion models and their singular limits
    • H. BERESTYCKI, B. NICOLAENKO & B. SCHEURER, Traveling wave solutions to combustion models and their singular limits, SIAM J. Math. Anal., 16 (1985), 1207-1242.
    • (1985) SIAM J. Math. Anal. , vol.16 , pp. 1207-1242
    • Berestycki, H.1    Nicolaenko, B.2    Scheurer, B.3
  • 11
    • 0040095038 scopus 로고
    • PhD Thesis "Sur quelques problèmes d'analyse non linéaire avec applications à la combustion", Université de Paris VI
    • A. BONNET, Non-uniqueness for flame propagation when the Lewis number is less than 1, in PhD Thesis "Sur quelques problèmes d'analyse non linéaire avec applications à la combustion", Université de Paris VI, 1992.
    • (1992) Non-Uniqueness for Flame Propagation When the Lewis Number Is Less Than 1
    • Bonnet, A.1
  • 12
  • 15
    • 0001056317 scopus 로고
    • Bifurcation from simple eigenvalues
    • M. G. CRANDALL & P. H. RABINOWITZ, Bifurcation from simple eigenvalues, J. Func. Anal., 8 (1971), 321-340.
    • (1971) J. Func. Anal. , vol.8 , pp. 321-340
    • Crandall, M.G.1    Rabinowitz, P.H.2
  • 16
    • 0015746829 scopus 로고
    • Bifurcation, pertubation of simple eigenvalues, and linearized stability
    • M. G. CRANDALL & P. H. RABINOWITZ, Bifurcation, pertubation of simple eigenvalues, and linearized stability, Arch. Rational Mech. Anal., 52 (1973), 161-180.
    • (1973) Arch. Rational Mech. Anal. , vol.52 , pp. 161-180
    • Crandall, M.G.1    Rabinowitz, P.H.2
  • 17
    • 0026997895 scopus 로고
    • Numerical study of thermal-diffusive instability of premixed flames
    • B. DENET & P. HALDENWANG, Numerical study of thermal-diffusive instability of premixed flames, Combust. Sci. Techn., 86 (1992), 199-121.
    • (1992) Combust. Sci. Techn. , vol.86 , pp. 199-1121
    • Denet, B.1    Haldenwang, P.2
  • 18
    • 0016578299 scopus 로고
    • Nerve axon equations IV: The stable and unstable impulse
    • J. W. EVANS, Nerve axon equations IV: the stable and unstable impulse, Indiana Univ. Math. J., 24 (1975), 1169-1190.
    • (1975) Indiana Univ. Math. J. , vol.24 , pp. 1169-1190
    • Evans, J.W.1
  • 19
    • 0001398111 scopus 로고
    • Nonadiabatic planar laminar flames and their singular limits
    • V. GIOVANGIGLI, Nonadiabatic planar laminar flames and their singular limits, SIAM. J. Math. Anal., 21 (1990), 1305-1325.
    • (1990) SIAM. J. Math. Anal. , vol.21 , pp. 1305-1325
    • Giovangigli, V.1
  • 20
    • 84974750400 scopus 로고
    • Etude d'une limite singulière d'un modèle intervenant en combustion
    • L. GLANGETAS, Etude d'une limite singulière d'un modèle intervenant en combustion, Asymptotic Analysis, 5 (1992), 317-342.
    • (1992) Asymptotic Analysis , vol.5 , pp. 317-342
    • Glangetas, L.1
  • 23
    • 0018479738 scopus 로고
    • Linear stability analysis of non adiabatic flames: Diffusional thermal model
    • G. JOULIN & P. CLAVIN, Linear stability analysis of non adiabatic flames: diffusional thermal model, Combust. Flame, 35 (1979), 139-153.
    • (1979) Combust. Flame , vol.35 , pp. 139-153
    • Joulin, G.1    Clavin, P.2
  • 24
    • 0020921541 scopus 로고
    • Nonlinear stability and bifurcation in the transition from laminar to turbulent flame propagation
    • S. B. MARGOLIS & B. J. MATKOWSKY, Nonlinear stability and bifurcation in the transition from laminar to turbulent flame propagation, Comb. Sci. Techn., 34 (1983), 44-77.
    • (1983) Comb. Sci. Techn. , vol.34 , pp. 44-77
    • Margolis, S.B.1    Matkowsky, B.J.2
  • 25
    • 0038910712 scopus 로고
    • Qualitative properties of a nonlinear system for laminar flames without ignition temperature
    • M. MARION, Qualitative properties of a nonlinear system for laminar flames without ignition temperature, Nonlinear Analysis, TMA, 9 (1985), 1269-1292.
    • (1985) Nonlinear Analysis, TMA , vol.9 , pp. 1269-1292
    • Marion, M.1
  • 26
    • 0005556128 scopus 로고
    • Pertubazione dello spettro di un operator? ellittico di tipo variazionale
    • A. M. MICHELETTI, Pertubazione dello spettro di un operator? ellittico di tipo variazionale, Ann. Mat. Pura Appl., 4 (1973), 267-281.
    • (1973) Ann. Mat. Pura Appl. , vol.4 , pp. 267-281
    • Micheletti, A.M.1
  • 27
    • 0013322639 scopus 로고
    • Singular limit analysis of stability of travelling wave solutions in bistable reaction-diffusion systems
    • Y. NISHIURA, M. MIMURA, H. IKEDA, H. FUJII, Singular limit analysis of stability of travelling wave solutions in bistable reaction-diffusion systems, SIAM J. Math. Anal., 21 (1990), 85-122.
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 85-122
    • Nishiura, Y.1    Mimura, M.2    Ikeda, H.3    Fujii, H.4
  • 28
    • 0009297310 scopus 로고
    • Asymptotic expansions of solutions of ordinary differential equations in Hilbert space
    • A. PAZY, Asymptotic expansions of solutions of ordinary differential equations in Hilbert space. Arch. Rational Mech. Anal., 24 (1967), 193-218.
    • (1967) Arch. Rational Mech. Anal. , vol.24 , pp. 193-218
    • Pazy, A.1
  • 30
    • 34249834157 scopus 로고
    • Stability of travelling fronts in a model for flame propagation, part II: Nonlinear stability
    • J. M. ROQUEJOFFRE, Stability of travelling fronts in a model for flame propagation, Part II: Nonlinear stability, Arch. Rational Mech. Anal., 117 (1992), 119-153.
    • (1992) Arch. Rational Mech. Anal. , vol.117 , pp. 119-153
    • Roquejoffre, J.M.1
  • 31
    • 0040835452 scopus 로고    scopus 로고
    • The asymptotic stability of a travelling wave solution arising from a combustion model
    • to appear
    • J. M. ROQUEJOFFRE & D. TERMAN, The asymptotic stability of a travelling wave solution arising from a combustion model, Nonlinear Analysis, TMA, to appear.
    • Nonlinear Analysis, TMA
    • Roquejoffre, J.M.1    Terman, D.2
  • 32
    • 0000814275 scopus 로고
    • Stability of waves of nonlinear parabolic equations
    • D. H. SATTINGER, Stability of waves of nonlinear parabolic equations, Adv. Math., 22 (1976), 312-355.
    • (1976) Adv. Math. , vol.22 , pp. 312-355
    • Sattinger, D.H.1
  • 33
    • 0020592802 scopus 로고
    • Instabilities, pattern formation and turbulence inflames
    • G. I. SIVASHINSKY, Instabilities, pattern formation and turbulence inflames, Ann. Rev. Fluid Mech., 15 (1993), 179-199.
    • (1993) Ann. Rev. Fluid Mech. , vol.15 , pp. 179-199
    • Sivashinsky, G.I.1
  • 34
    • 0018467679 scopus 로고
    • On self-turbulization of a laminar flame
    • G. I. SIVASHINSKY, On self-turbulization of a laminar flame, Acta Astronaut., 6 (1979), 569-591.
    • (1979) Acta Astronaut. , vol.6 , pp. 569-591
    • Sivashinsky, G.I.1
  • 35
    • 84967728255 scopus 로고
    • Generation of analytic semigroups by strongly elliptic operators under general boundary conditons
    • H. B. STEWART, Generation of analytic semigroups by strongly elliptic operators under general boundary conditons, Trans. Am. Math. Soc., 259 (1980), 299-310.
    • (1980) Trans. Am. Math. Soc. , vol.259 , pp. 299-310
    • Stewart, H.B.1
  • 36
    • 0040688532 scopus 로고
    • Stability of planar wave solutions to a combustion model
    • D. TERMAN, Stability of planar wave solutions to a combustion model, SIAM J. Math. Anal., 21 (1990), 1139-1171.
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 1139-1171
    • Terman, D.1
  • 37
    • 0002944097 scopus 로고
    • Application of the rotation theory of vector fields to the study of wave solutions of parabolic equations
    • A. I. VOLPERT & V. A. VOLPERT, Application of the rotation theory of vector fields to the study of wave solutions of parabolic equations, Trans. Moscow Math. Soc. (1990), 59-108.
    • (1990) Trans. Moscow Math. Soc. , pp. 59-108
    • Volpert, A.I.1    Volpert, V.A.2
  • 38
    • 0040688527 scopus 로고
    • Applications of the theory of bifurcations to the study of nonstationary combustion regimes
    • V. A. VOLPERT, A. I. VOLPERT & A. G. MERZHANOV, Applications of the theory of bifurcations to the study of nonstationary combustion regimes, Dokl. Akad. Nauk. USSR, 163 (1982), 435-438.
    • (1982) Dokl. Akad. Nauk. USSR , vol.163 , pp. 435-438
    • Volpert, V.A.1    Volpert, A.I.2    Merzhanov, A.G.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.