메뉴 건너뛰기




Volumn 198, Issue 3, 2010, Pages 981-1030

Stability of Gasless Combustion Fronts in One-Dimensional Solids

Author keywords

[No Author keywords available]

Indexed keywords


EID: 78049292290     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-010-0358-y     Document Type: Article
Times cited : (27)

References (40)
  • 1
    • 34247577468 scopus 로고    scopus 로고
    • High Lewis number combustion wavefronts: a perturbative Melnikov analysis
    • Balasuriya S., Gottwald G., Hornibrook J., Lafortune S.: High Lewis number combustion wavefronts: a perturbative Melnikov analysis. SIAM J. Appl. Math. 67, 464-486 (2007).
    • (2007) SIAM J. Appl. Math. , vol.67 , pp. 464-486
    • Balasuriya, S.1    Gottwald, G.2    Hornibrook, J.3    Lafortune, S.4
  • 3
    • 0025413863 scopus 로고
    • Two routes to chaos in condensed phase combustion
    • Bayliss A., Matkowsky B.: Two routes to chaos in condensed phase combustion. SIAM J. Appl. Math. 50, 437-459 (1990).
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 437-459
    • Bayliss, A.1    Matkowsky, B.2
  • 4
    • 64149094353 scopus 로고    scopus 로고
    • Nonlinear convective stability of traveling fronts near Turing and Hopf instabilities
    • Beck M., Ghazaryan A., Sandstede B.: Nonlinear convective stability of traveling fronts near Turing and Hopf instabilities. J. Differ. Equ. 246, 4371-4390 (2009).
    • (2009) J. Differ. Equ. , vol.246 , pp. 4371-4390
    • Beck, M.1    Ghazaryan, A.2    Sandstede, B.3
  • 6
    • 78049240719 scopus 로고
    • Mathematical investigation of the cold boundary difficulty in flame propagation theory
    • Minneapolis, MN, 1989, IMA Vol. Math. Appl., Springer, New York
    • Berestycki, H., Larrouturou, B., Roquejoffre, J.-M.: Mathematical investigation of the cold boundary difficulty in flame propagation theory. Dynamical Issues in Combustion Theory, Vol. 35 (Minneapolis, MN, 1989) IMA Vol. Math. Appl., Springer, New York, 37-61, 1991.
    • (1991) Dynamical Issues in Combustion Theory , vol.35 , pp. 37-61
    • Berestycki, H.1    Larrouturou, B.2    Roquejoffre, J.-M.3
  • 7
    • 64549123053 scopus 로고    scopus 로고
    • Nonlinear stability of rotating patterns
    • Beyn W. J., Lorenz J.: Nonlinear stability of rotating patterns. Dyn. Partial Differ. Equ. 5, 349-400 (2008).
    • (2008) Dyn. Partial Differ. Equ. , vol.5 , pp. 349-400
    • Beyn, W.J.1    Lorenz, J.2
  • 8
    • 0347997366 scopus 로고    scopus 로고
    • Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms
    • Billingham J.: Phase plane analysis of one-dimensional reaction diffusion waves with degenerate reaction terms. Dyn. Stab. Syst. 15, 23-33 (2000).
    • (2000) Dyn. Stab. Syst. , vol.15 , pp. 23-33
    • Billingham, J.1
  • 9
    • 0003327379 scopus 로고    scopus 로고
    • Evolution Semigroups in Dynamical Systems and Differential Equations
    • AMS, Providence
    • Chicone, C., Latushkin, Y.: Evolution Semigroups in Dynamical Systems and Differential Equations. Math. Surv. Monogr. Vol. 70. AMS, Providence, 1999.
    • (1999) Math. Surv. Monogr , vol.70
    • Chicone, C.1    Latushkin, Y.2
  • 10
    • 33749349188 scopus 로고    scopus 로고
    • Combustion fronts in a porous medium with two layers
    • da Mota J. C., Schecter S.: Combustion fronts in a porous medium with two layers. J. Dyn. Differ. Equ. 18, 615-665 (2006).
    • (2006) J. Dyn. Differ. Equ. , vol.18 , pp. 615-665
    • da Mota, J.C.1    Schecter, S.2
  • 11
    • 33749528149 scopus 로고    scopus 로고
    • Wave sequences for solid fuel adiabatic in-situ combustion in porous media
    • de Souza A. J., Akkutlu I. Y., Marchesin D.: Wave sequences for solid fuel adiabatic in-situ combustion in porous media. Comput. Appl. Math. 25, 27-54 (2006).
    • (2006) Comput. Appl. Math. , vol.25 , pp. 27-54
    • de Souza, A.J.1    Akkutlu, I.Y.2    Marchesin, D.3
  • 12
    • 0001058067 scopus 로고
    • Numerical computation of heteroclinic orbits. Continuation techniques and bifurcation problems
    • Doedel E., Friedman M. J.: Numerical computation of heteroclinic orbits. Continuation techniques and bifurcation problems. J. Comput. Appl. Math. 26, 155-170 (1989).
    • (1989) J. Comput. Appl. Math. , vol.26 , pp. 155-170
    • Doedel, E.1    Friedman, M.J.2
  • 15
    • 0001472246 scopus 로고
    • Nerve axon equations. III. Stability of the nerve impulse
    • Evans, J. W.: Nerve axon equations. III. Stability of the nerve impulse. Indiana Univ. Math. J. 22, 577-593(1972/73).
    • (1972) Indiana Univ. Math. J , vol.22 , pp. 577-593
    • Evans, J.W.1
  • 16
    • 0010573332 scopus 로고    scopus 로고
    • Solitary waves on FPU lattices: II. Linear implies nonlinear stability
    • Friesecke G., Pego R. L.: Solitary waves on FPU lattices: II. Linear implies nonlinear stability. Nonlinearity 15, 1343-1359 (2002).
    • (2002) Nonlinearity , vol.15 , pp. 1343-1359
    • Friesecke, G.1    Pego, R.L.2
  • 17
    • 1042302649 scopus 로고    scopus 로고
    • Stable transport of information near essentially unstable localized structures
    • Gallay T., Schneider G., Uecker H.: Stable transport of information near essentially unstable localized structures. Discret. Contin. Dyn. Syst. Ser. B 4, 349-390 (2004).
    • (2004) Discret. Contin. Dyn. Syst. Ser. B , vol.4 , pp. 349-390
    • Gallay, T.1    Schneider, G.2    Uecker, H.3
  • 18
    • 70349174141 scopus 로고    scopus 로고
    • On the convective nature of the instability of a front undergoing a supercritical Turing bifurcation
    • Ghazaryan G.: On the convective nature of the instability of a front undergoing a supercritical Turing bifurcation. Math. Comput. Simul. 80, 10-19 (2009).
    • (2009) Math. Comput. Simul. , vol.80 , pp. 10-19
    • Ghazaryan, G.1
  • 19
    • 64149104786 scopus 로고    scopus 로고
    • Nonlinear stability of high Lewis number combustion fronts
    • Ghazaryan G.: Nonlinear stability of high Lewis number combustion fronts. Indiana Univ. Math. J. 58, 181-212 (2009).
    • (2009) Indiana Univ. Math. J. , vol.58 , pp. 181-212
    • Ghazaryan, G.1
  • 20
    • 57249110716 scopus 로고    scopus 로고
    • Nonlinear convective instability of Turing-unstable fronts near onset: a case study
    • Ghazaryan G., Sandstede B.: Nonlinear convective instability of Turing-unstable fronts near onset: a case study. SIAM J. Appl. Dyn. Syst. 6, 319-347 (2007).
    • (2007) SIAM J. Appl. Dyn. Syst. , vol.6 , pp. 319-347
    • Ghazaryan, G.1    Sandstede, B.2
  • 21
    • 0003304963 scopus 로고
    • Geometric Theory of Semilinear Parabolic Equations
    • Springer, Berlin-New York
    • Henry, D.: Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Mathematics, Vol. 840. Springer, Berlin-New York, 1981.
    • (1981) Lecture Notes in Mathematics , vol.840
    • Henry, D.1
  • 22
    • 58149347401 scopus 로고    scopus 로고
    • Counter-propagating two-soliton solutions in the Fermi-Pasta-Ulam lattice
    • Hoffman A., Wayne C. E.: Counter-propagating two-soliton solutions in the Fermi-Pasta-Ulam lattice. Nonlinearity 21, 2911-2947 (2008).
    • (2008) Nonlinearity , vol.21 , pp. 2911-2947
    • Hoffman, A.1    Wayne, C.E.2
  • 24
    • 0030736402 scopus 로고    scopus 로고
    • Mathematical analysis of a condensed phase combustion model without ignition temperature
    • Logak E.: Mathematical analysis of a condensed phase combustion model without ignition temperature. Nonlinear Anal. Theory Methods Appl. 28, 1-38 (1997).
    • (1997) Nonlinear Anal. Theory Methods Appl. , vol.28 , pp. 1-38
    • Logak, E.1
  • 26
    • 0018031317 scopus 로고
    • Propagation of a pulsating reaction front in solid fuel combustion
    • Matkowsky B., Sivashinsky G.: Propagation of a pulsating reaction front in solid fuel combustion. SIAM J. Appl. Math. 35, 465-478 (1978).
    • (1978) SIAM J. Appl. Math. , vol.35 , pp. 465-478
    • Matkowsky, B.1    Sivashinsky, G.2
  • 27
    • 0030558727 scopus 로고    scopus 로고
    • Asymptotic stability of solitary waves for the regularized long-wave equation
    • Miller J. R., Weinstein M. I.: Asymptotic stability of solitary waves for the regularized long-wave equation. Commun. Pure Appl. Math. 49, 399-441 (1996).
    • (1996) Commun. Pure Appl. Math. , vol.49 , pp. 399-441
    • Miller, J.R.1    Weinstein, M.I.2
  • 28
    • 48549112859 scopus 로고
    • Exponential dichotomies and transversal homoclinic points
    • Palmer K.: Exponential dichotomies and transversal homoclinic points. J. Differ. Equ. 55, 225-256 (1984).
    • (1984) J. Differ. Equ. , vol.55 , pp. 225-256
    • Palmer, K.1
  • 29
    • 84968484465 scopus 로고
    • Exponential dichotomies and Fredholm operators
    • Palmer K.: Exponential dichotomies and Fredholm operators. Proc. Am. Math. Soc. 104, 149-156 (1988).
    • (1988) Proc. Am. Math. Soc. , vol.104 , pp. 149-156
    • Palmer, K.1
  • 31
    • 21844510556 scopus 로고
    • Asymptotic stability of solitary waves
    • Pego R. L., Weinstein M. I.: Asymptotic stability of solitary waves. Commun. Math. Phys. 164, 305-349 (1994).
    • (1994) Commun. Math. Phys. , vol.164 , pp. 305-349
    • Pego, R.L.1    Weinstein, M.I.2
  • 32
    • 67649363651 scopus 로고    scopus 로고
    • Stability of travelling waves
    • North-Holland, Amsterdam
    • Sandstede, B.: Stability of travelling waves. Handbook of Dynamical Systems, Vol. 2. North-Holland, Amsterdam, 983-1055, 2002.
    • (2002) Handbook of Dynamical Systems , vol.2 , pp. 983-1055
    • Sandstede, B.1
  • 33
    • 0346686985 scopus 로고    scopus 로고
    • Absolute and convective instabilities of waves on unbounded and large bounded domains
    • Sandstede, B., Scheel, A. Absolute and convective instabilities of waves on unbounded and large bounded domains. Physica D145, 233-277.
    • Physica D , vol.145 , pp. 233-277
    • Sandstede, B.1    Scheel, A.2
  • 34
    • 41649118430 scopus 로고    scopus 로고
    • Relative Morse indices, Fredholm indices, and group velocities
    • Sandstede B., Scheel A.: Relative Morse indices, Fredholm indices, and group velocities. Discret. Contin. Dyn. Syst. 20, 139-158 (2008).
    • (2008) Discret. Contin. Dyn. Syst. , vol.20 , pp. 139-158
    • Sandstede, B.1    Scheel, A.2
  • 35
    • 0001449766 scopus 로고
    • The saddle-node separatrix-loop bifurcation
    • Schecter S.: The saddle-node separatrix-loop bifurcation. SIAM J. Math. Anal. 18, 1142-1156 (1987).
    • (1987) SIAM J. Math. Anal. , vol.18 , pp. 1142-1156
    • Schecter, S.1
  • 36
    • 0242689013 scopus 로고    scopus 로고
    • Dynamics of evolutionary equations
    • Springer, New York
    • Sell, G., You, Y.: Dynamics of evolutionary equations. Applied Mathematical Sciences, Vol. 143, Springer, New York, 2002.
    • (2002) Applied Mathematical Sciences , vol.143
    • Sell, G.1    You, Y.2
  • 37
    • 0036588787 scopus 로고    scopus 로고
    • Linear stability of a plane front in solid combustion at large heat of reaction
    • Varas F., Vega J.: Linear stability of a plane front in solid combustion at large heat of reaction. SIAM J. Appl. Math. 62, 1810-1822 (2002).
    • (2002) SIAM J. Appl. Math. , vol.62 , pp. 1810-1822
    • Varas, F.1    Vega, J.2
  • 39
    • 33748579233 scopus 로고    scopus 로고
    • Stability of travelling waves with algebraic decay for n-degree Fisher-type equations
    • Wu Y., Xing X., Ye Q.: Stability of travelling waves with algebraic decay for n-degree Fisher-type equations. Discret. Contin. Dyn. Syst. 16, 47-66 (2006).
    • (2006) Discret. Contin. Dyn. Syst. , vol.16 , pp. 47-66
    • Wu, Y.1    Xing, X.2    Ye, Q.3
  • 40
    • 38249015307 scopus 로고
    • Melnikov vector in higher dimensions
    • Yamashita M.: Melnikov vector in higher dimensions. Nonlinear Anal. 18, 657-670 (1992).
    • (1992) Nonlinear Anal. , vol.18 , pp. 657-670
    • Yamashita, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.