1. G.I. Barenblatt, Y.B. Zeldovich, A.G Istratov, “On diffusional thermal instability of laminar flame”, Prikl. Mekh. Tekh. Fiz.2, 21–26, 1962.

   Google Scholar 

2. R.N. Buchal, J.B, Keller, “Boundary layer problems in diffraction theory”, Comm. Pure Appl. Math.13: 85–114, 1960.

   MathSciNet MATH  Google Scholar 

3. A.G. Class, B.J. Matkowsky, A.Y. Klimenko, “A Unified Model of Flames as Gasdynamic Discontinuities”, J. Fluid Mech.,491: 11–49, 2003.

   Article MathSciNet MATH  Google Scholar 

4. A.G. Class, B.J. Matkowsky, A.Y. Klimenko, “Stability of planar flames as gasdynamic discontinuities”. J. Fluid Mech.,491: 51–63, 2003.

   Article MathSciNet MATH  Google Scholar 

5. P. Clavin, F.A. Williams, “Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scales and low intensity”, J. Fluid. Mech.116: 251–282, 1982.

   Article MATH  Google Scholar 

6. G. Darrieus, “Propagation d’un front de flamme”, Presented at La Technique Moderne and Le Congrés de Mechanique Appliquée, Paris, 1938 and 1945.

   Google Scholar 

7. W. Eckhaus, “Theory of flame-front stability”, J. Fluid Mech.10: 80–100, 1961.

   Article MathSciNet MATH  Google Scholar 

8. J.W. Gibbs, “On the equilibrium of heterogeneous substances”, Trans. Conn. Acad.3: 108–248, 1876 and 343–524, 1878.

   Google Scholar 

9. J.W. Gibbs, “Abstract of ‘on the equilibrium of heterogeneous substances”’, Amer. J. Sci., ser. 3,18: 277–293 and 371–387, 1879.

   Google Scholar 

10. A. Golovin, B.J. Matkowsky, A. Bayliss, A. Nepomnyashchy, “Coupled KS-CGL and coupled Burgers-CGL equations for flames governed by a sequential reaction”, PhysicaD 129: 253–298, 1999.

    Google Scholar 

11. A. Golovin, B.J. Matkowsky, A. Nepomnyashchy, “A complex SwiftHohenberg equation coupled to the Goldstone mode in the nonlinear dynamics of flames”, PhysicaD 179: 183–210, 2003.

    Google Scholar 

12. G.J. Habetler, B.J. Matkowsky, “Uniform asymptotic expansions in transport theory with small mean free paths and the diffusion approximation”, J. Math. Phys.16: 846–854, 1975.

    Article MathSciNet MATH  Google Scholar 

13. B. Karlovitz, D.W. Denniston, H.D. Knapschaefer, F.E. Wells, “Studies on turbulent flames”, Fourth Symposium (Int.) on Combustion, The Combustion Institute, 613–620, 1953.

    Google Scholar 

14. J.B. Keller, “Rays, waves and asymptotics”, Bull. Amer. Math. Soc.84: 727–750, 1978.

    Article MathSciNet MATH  Google Scholar 

15. J.B. Keller, S. Antman, (eds.), Bifurcation theory of nonlinear eigenvalue problems, Benjamin, 1969.

    Google Scholar 

16. J.B. Keller, R.M. Lewis, “Asymptotic methods for partial differential equations: the reduced wave equation and Maxwell’s equations”, in Surveys in Applied Mathematics1, J.B. Keller, D.W. McLaughlin, G.C. Papanicolaou, eds. Plenum, 1995.

    Google Scholar 

17. J.B. Keller, R.M. Lewis, “Asymptotic methods for partial differential equations: the reduced wave equation and Maxwell’s equations”, Courant Institute Research Report EM-194, 1964.

    Google Scholar 

18. J.B. Keller, S.I. Rubinow, “Asymptotic solution of eigenvalue problems”, Ann. Phys.9: 24–75, 1960.

    Article MATH  Google Scholar 

19. ] J.B. Keller, M.L. Weitz, “A Theory of Thin Jets”, Proc. Ninth Int’l. Cong. Appl. Mech.1, 316–323. Brussels, Belgium, 1957.

    Google Scholar 

20. J.B. Keller, M.L. Weitz, “Thin Unsteady Heavy Jets”, Report IMMNYU 186 - Inst. Math. Sci., New York Univ., 1952.

    Google Scholar 

21. A.Y. Klimenko, A.G. Class, “On premixed flames as gasdynamic discontinuities: A simple approach to derive their propagation speed”, Comb. Sci. and Tech.160: 25–37, 2000.

    Article  Google Scholar 

22. C. Knessl, B.J. Matkowsky, Z. Schuss, C. Tier, “An asymptotic theory of large deviations for Markov jump processes”, SIAM J. Appl. Math45: 1006–1028, 1985.

    MathSciNet MATH  Google Scholar 

23. L.D. Landau, “On the theory of slow combustion”, Acta Physicochimic URSS19: 77–85, 1944.

    Google Scholar 

24. G.H. Markstein, “Experimental and theoretical studies of flame front stability”, J. Aero. Sci.18: 199–209, 1951.

    Google Scholar 

25. G.H. Markstein, ed., Nonsteady flame propagation, Pergamon, 1964.

    Google Scholar 

26. M. Matalon, B.J. Matkowsky, “Flames as gasdynamic discontinuities”, J. Fluid Mech.124: 239–259, 1982.

    Article MATH  Google Scholar 

27. M. Matalon, B.J. Matkowsky, “On the stability of plane and curved flames”, SIAM J. Appl. Math.44: 327–343, 1984.

    MathSciNet MATH  Google Scholar 

28. B.J. Matkowsky, Z. Schuss, C. Knessl, C. Tier, M. Mangel, “Asymptotic solution of the Kramers Moyal equation and first passage times for Markov jump processes”, Phys. RevA 29: 3359–3369, 1984.

    Google Scholar 

29. B.J. Matkowsky, G.I. Sivashinsky, “An asymptotic derivation of two models in flame theory associated with the constant density approximation”, SIAM J. Appl. Math.37: 686–699, 1979.

    MathSciNet MATH  Google Scholar 

30. B.J. Matkowsky, V.A. Volpert, “Nonlocal amplitude equations in reaction diffusion systems” Random and Comp. Dyn.1: 33–58, 1992.

    MathSciNet  Google Scholar 

31. M.H. Millman, J.B. Keller, “Perturbation theory of nonlinear boundary value problems”, J. Math. Phys.10: 342–361, 1969.

    Article MathSciNet MATH  Google Scholar 

32. P. Pelce, P. Clavin, “Influence of hydrodynamics and diffusion upon the stability limits of laminar premixed flames”, J. Fluid Mech.124: 219–237, 1982.

    Article MATH  Google Scholar 

33. G.I. Sivashinsky, “On a distorted flame front as a hydrodynamic discontinuity”, Acta Astronautica3: 889–918, 1976.

    Article MathSciNet  Google Scholar 

34. G.I. Sivashinsky, “On flame propagation under conditions of stoichiometry”, SIAM J. Appl. Math.39: 67–82, 1980.

    MathSciNet MATH  Google Scholar 

35. Y.B. Zeldovich, G.I. Barenblatt, V.B, Librovich, G.M. Makhviladze, The mathematical theory of combustion and explosions, Consultants Bureau, 1985.

    Google Scholar 

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