Evans function analysis of the stability of non-adiabatic flames

References

• Alexander , J , Gardner , R and Jones , C . 1990 . A topological invariant arising in the stability analysis of travelling waves . J. Reine Angew. Math. , 410 : 167 – 212 .
   Web of Science ®Google Scholar
• Balmforth , N J , Craster , R V and Malham , S J A . 1999 . Unsteady fronts in an autocatalytic system . Proc. R. Soc. , 455 : 1401 – 33 . A
   Google Scholar
• Bayliss , A and Matkowsky , B J . 1990 . Two routes to chaos in condensed phase combustion . SIAM J. Appl. Math. , 50 : 437 – 59 .
   Web of Science ®Google Scholar
• Beyn , W J and Lorenz , J . 1999 . Stability of traveling waves: dichotomies and eigenvalue conditions on finite intervals . Numer. Func. Anal. Optim. , 20 : 201 – 44 .
   Web of Science ®Google Scholar
• Billingham , J and Mercer , G N . 2001 . The effect of heat loss on the propagation of strongly exothermic combustion waves . Combust. Theory Modelling , 5 : 319 – 42 .
   Web of Science ®Google Scholar
• Brin , L Q . 2001 . Numerical testing of the stability of viscous shock waves . Math. Comput. , 70 : 1071 – 88 .
   Web of Science ®Google Scholar
• Buckmaster , J D . 1976 . The quenching of deflagration waves . Combust. Flame , 26 : 151 – 62 .
   Web of Science ®Google Scholar
• Coppel , W A . 1978 . Dichotomies in Stability Theory , Berlin : Springer . (Lecture Notes in Mathematics vol 629)
   Google Scholar
• Dold , J W , Thatcher , R W and Shah , A A . 2003 . High order effects in one step reaction sheet jump conditions for premixed flames . Combust. Theory Modelling , 7 : 109 – 27 .
   Web of Science ®Google Scholar
• Eastham , M S P . 1989 . The Asymptotic Solution of Linear Differential Systems , Oxford : Clarendon .
   Google Scholar
• Evans , J W . 1974/75 . Nerve axon equations IV: the stable and unstable impulse . Indiana Univ. Math. J. , 24 : 1169 – 90 .
   Web of Science ®Google Scholar
• Gardner , R A and Zumbrun , K . 1998 . The gap lemma and geometric criteria for instability of viscous shock profiles . Commun. Pure Appl. Math. , 51 : 797 – 855 .
   Web of Science ®Google Scholar
• Giovangigli , V . 1990 . Nonadiabatic plane laminar flames and their singular limits . SIAM J. Math. Anal. , 21 : 1305 – 25 .
   Web of Science ®Google Scholar
• Giovangigli , V . 1999 . Multicomponent Flow Modeling , Boston : Birkhäuser .
   Google Scholar
• Giovangigli , V and Smooke , M D . 1992 . Application of continuation methods to plane premixed laminar flames . Combust. Sci. Technol. , 87 : 241 – 56 .
   Web of Science ®Google Scholar
• Govaerts , W J F . 2000 . Numerical Methods for Bifurcations of Dynamical Equilibria , SIAM
   Google Scholar
• Henry , D . 1981 . Geometric Theory of Semilinear Parabolic Equations , Berlin : Springer .
   Google Scholar
• Hoff , D and Zumbrun , K . 2000 . Asymptotic behavior of multidimensional scalar viscous shock fronts . Indiana Univ. Math. J. , 49 : 427 – 74 .
   Web of Science ®Google Scholar
• Joulin , G and Clavin , P . 1979 . Linear stability analysis of nonadiabatic flames: diffusional-thermal model . Combust. Flame , 35 : 139 – 53 .
   Web of Science ®Google Scholar
• Ju , Y , Gou , H , Maruta , K and Liu , F . 1997 . On the extinction limit and flammability limit of non-adiabatic stretched methane-air premixed flames . J. Fluid Mech. , 342 : 315 – 34 .
   Web of Science ®Google Scholar
• Kee , R J , Grcar , J F , Smooke , M D and Miller , J A . 1985 . A Fortran program for modeling steady laminar one-dimensional premixed flames . Sandia Report , SAND85-8240
   Google Scholar
• Keller , H B . 1968 . Numerical Methods for Two-Point Boundary-Value Problems , MA: Boston : Blaisdell .
   Google Scholar
• Keller , H B . 1977 . “ Numerical solution of bifurcation and nonlinear eigenvalue problems ” . In Applications of Bifurcation Theory , Edited by: Rabinowitz , P . 359 – 84 . New York : Academic .
   Google Scholar
• Kuznecov , Y A . 1995 . Elements of Applied Bifurcation Theory , New York : Springer .
   Google Scholar
• Lasseigne , D G , Jackson , T L and Jameson , L . 1999 . Stability of freely propagating flames revisited . Combust. Theory Modelling , 3 : 591 – 611 .
   Web of Science ®Google Scholar
• Law , C K and Egolfopoulos , F N . 1992 . A unified chain-thermal theory of fundamental flammability limits . Proc. Combust. Inst. , 24 : 137 – 44 .
   Google Scholar
• Matkowsky , B J and Sivashinsky , G I . 1978 . Propagation of a pulsating reaction front in solid fuel combustion . SIAM J. Appl. Math. , 35 : 465 – 78 .
   Web of Science ®Google Scholar
• Pego , R L and Weinstein , M I . 1992 . Eigenvalues and instabilities of solitary waves . Phil. Trans. R. Soc. Ser. , 340 : 47 – 94 . A
   Web of Science ®Google Scholar
• Sandstede , B and Scheel , A . 2001 . On the structure of spectra of modulated travelling waves . Math. Nachr. , 232 : 39 – 93 .
   Web of Science ®Google Scholar
• Simon , P L , Kalliadasis , S , Merkin , J H and Scott , S K . 2002 . Quenching of flame propagation with heat loss . J. Math. Chem. , 31 : 313 – 32 .
   Web of Science ®Google Scholar
• Sivashinsky , G I . 1977 . Diffusional-thermal theory of cellular flames . Combust. Sci. Technol. , 15 : 137 – 46 .
   Web of Science ®Google Scholar
• Volpert , A I , Volpert , V A and Volpert , V A . 1994 . Traveling Wave Solutions of Parabolic Systems , New York : AMS .
   Google Scholar
• Warnatz , J , Maas , U and Dibble , R W . 2001 . Combustion. Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation , Berlin : Springer .
   Google Scholar
• Weber , R O , Mercer , G N , Sidhu , H S and Gray , B F . 1997 . Combustion waves for gases (Le = 1) and solids (Le → ∞) . Proc. R. Soc. Ser. , 453 : 1105 – 18 . A
   Web of Science ®Google Scholar
• Williams , F A . 1985 . Combustion Theory , London : Addison-Wesley .
   Google Scholar
• Zeldovich , Ya B , Barenblatt , G I , Librovich , V B and Makhviladze , G M . 1985 . The Mathematical Theory of Combustion and Explosions , New York : Consultants Bureau .
   Google Scholar