no. 5
Travelling fronts in cylinders
Annales de l'I.H.P. Analyse non linéaire, Tome 9 (1992) no. 5, pp. 497-572. 
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Berestycki, Henri; Nirenberg, Louis. Travelling fronts in cylinders. Annales de l'I.H.P. Analyse non linéaire, Tome 9 (1992) no. 5, pp. 497-572. http://www.numdam.org/item/AIHPC_1992__9_5_497_0/

[AN] S. Agmon, and L. Nirenberg, Properties of Solutions of Ordinary Differential Equations in Banach Space, Comm. Pure Appl. Math., Vol. 16, 1963, pp. 121-239. | MR | Zbl

[AW1] D.G. Aronson and H.F. Weinberger, Nonlinear Diffusion in Population Genetics, Combustion and Nerve Propagation, in "Partial Differential Equations and Related Topics", J. A. GOLDSTEIN Ed., Lecture Notes in Math., No. 446, Springer-Verlag, New York, 1975, pp. 5-49. | MR | Zbl

[AW2] D.G. Aronson and H.F. Weinberger, Multidimensional Nonlinear Diffusions Arising in Population Genetics, Adv. in Math., Vol. 30, 1978, pp. 33-58. | MR | Zbl

[BCN] H. Berestycki, L.A. Caffarelli and L. Nirenberg, Uniform Estimates for Regularization of Free Boundary Problems, Analysis and Partial Differential Equations, C. SADOSKY M. DECKER Ed., 1990, pp. 567-617. | MR | Zbl

[BL1] H. Berestycki and B. Larrouturou, A Semilinear Elliptic Equation in a Strip Arising in a Two-Dimensional Flame Propagation Model, J. Reine Angewandte Math., Vol. 396, 1989, pp. 14-40. | MR | Zbl

[BL2] H. Berestycki and B. Larrouturou, Mathematical Aspects of Planar Flame Propagation, Longman Press (in preparation).

[BLL] H. Berestycki, B. Larrouturou and P.-L. Lions, Multidimensional Traveling-Wave Solutions of a Flame Propagation Model, Arch. Rational Mech. Anal., Vol. 111, 1990, pp. 33-49. | MR | Zbl

[BLR] H. Berestycki, B. Larrouturou and J.M. Roquejoffre, Stability of Travelling Fronts in a Curved Flame Model, Part I. Linear Analysis, Arch. Rational. Mech. Anal., Vol. 117, 1991, pp. 97-117. | MR | Zbl

[BNS] H. Berestycki, B. Nicolaenko and B. Scheurer, Travelling Wave Solutions to Combustion Models and their Singular Limits, S.I.A.M. J. Math. Anal., Vol. 16, (6), 1985, pp. 1207-1242. | MR | Zbl

[BN1] H. Berestycki and L. Nirenberg, Some Qualitative Properties of Solutions of Semilinear Elliptic Equations in Cylindrical Domains, in Analysis, etc. (volume dedicated to J. Moser), P. H. RABINOWITZ and E. ZEHNDER Ed., Academic Press, New York, 1990, pp. 115-164. | MR | Zbl

[BN2] H. Berestycki and L. Nirenberg, Travelling Front Solutions of Semilinear Equations in Higher Dimensions, Frontiers in Pure and Appl. Math., R. DAUTRAY Ed., North-Holland, 1991, pp. 31-41. | MR | Zbl

[BN3] H. Berestycki and L. Nirenberg, On the Method of Moving Planes and the Sliding Method, Bol. da Soc. Brasileira de Matematica, Vol. 22, 1991, pp. 1-37. | MR | Zbl

[BN4] H. Berestycki and L. Nirenberg, Asymptotic Behaviour via the Harnack Inequality, Nonlinear Analysis.A tribute in Honour of Giovanni Prodi, A. AMBROSETTI et al. Ed., Sc. Normale Sup. Pisa, 1991, pp. 135-144. | MR | Zbl

[CH] R.G. Casten and C.J. Holland, Instability Results for Reaction-Diffusion Equations with Neumann Boundary Conditions, J. Diff. Eq., Vol. 27, 1978, pp. 266-273. | MR | Zbl

[Fi] P.C. Fife, Mathematical Aspects of Reacting and Diffusing Systems, Lect. Notes Biomath., No. 28, Springer-Verlag, New York, 1979. | MR | Zbl

[FM] P.C. Fife and J.B. Mcleod, The Approach of Solutions of Nonlinear Diffusion Equations to Travelling Front Solutions, Arch. Rat. Mech. Anal., Vol. 65, 1977, pp. 335-361. | MR | Zbl

[Fr1] M. Freidlin, Limit Theorems for Large Deviations and Reaction-Diffusion Equations, Ann. Prob., Vol. 13, 1985, pp. 639-675. | MR | Zbl

[Fr2] M. Freidlin, KPP in cylinders (to appear).

[G] R. Gardner, Existence of Multidimensional Traveling Wave Solutions of an Initial-Boundary Value Problem, J. Diff. Eq., Vol. 61, 1986, pp. 335-379. | MR | Zbl

[H] S. Heinze, Traveling Waves for Semilinear Parabolic Partial Differential Equations in Cylindrical Domains, preprint.

[JN] W.E. Johnson and W. Nachbar, Laminar Flame Theory and the Steady Linear Burning of a Monopropellant, Arch. Rat. Mech. Anal., Vol. 12, 1963, pp. 58-91. | MR | Zbl

[K1] Ja.I. Kanel', Stabilization of Solution of the Cauchy Problem for Equations Encountered in Combustion Theory, Mat. Sbornik, Vol. 59, 1962, pp. 245-288. | MR | Zbl

[K2] Ja I. Kanel',On Steady State Solutions to Systems of Equations Arising in Combustion Theory, Dokl. Akad. Nauk U.S.S.R., Vol. 149, 1963, pp. 367-369.

[KPP] A.N. Kolmogorov, I.G. Petrovsky and N.S. Piskunov, Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique, Bulletin Université d'État à Moscow (Bjul. Moskowskogo Gos. Univ.), Série internationale, section A. 1, 1937, pp. 1-26, English translation: Study of the Diffusion Equation with Growth of the Quantity of Matter and its Application to a Biology Problem. In Dynamics of curved fronts, R. PELCÉ Ed., Perspectives in Physics Series, Academic Press, New York, 1988, pp. 105-130. | Zbl

[L] P.D. Lax, A Phragmén-Lindelöf Theorem in Harmonic Analysis and its Applications to Some Questions in the Theory of Elliptic Equations, Comm. Pure Appl. Math., Vol. 10, 1957, pp. 361-389. | MR | Zbl

[M] H. Matano, Asymptotic Behavior and Stability of Solutions of Semilinear Diffusion Equations, Publ. R.I.M.S., Kyoto University, Vol. 15, 1979, pp.401-454. | MR | Zbl

[McK] H. Mckean, An Application of Brownian Motion to the Equation of Kolmogorov-Petrovskii-Piscounov, Comm. Pure Appl. Math., Vol. 28, 1975, pp.323-331; Vol. 29, 1976, pp. 553-554. | MR | Zbl

[O] O. Oleinik (to appear).

[P] A. Pazy, Asymptotic Expansions of Solutions of Ordinary Differential Equations in Hilbert Space, Arch. Rational. Mech. Anal., Vol. 24, 1967, pp. 193-218. | MR | Zbl

[R1] J.M. Roquejoffre, Stability of Travelling Fronts in a Curved Flame Model. Part II: Non-Linear Orbital Stability, Arch. Rational. Mech. Anal. (to appear). | MR

[R2] J.M. Roquejoffre, Convergence to Travelling Waves for Solutions of a Class of Semilinear Parabolic Equations (to appear). | MR | Zbl

[Ve1] J.M. Vega, The Asymptotic Behavior of the Solutions of Some Semilinear Elliptic Equations in Cylindrical Domains, J. Diff. Eqs. (submitted). | Zbl

[Ve2] J.M. Vega, Travelling Wavefronts of Reaction-Diffusion Equations in Cylindrical Domains, Comm. P.D.E. (submitted). | Zbl

[Vo1] A.I. Vol'Pert, On the Propagation of Waves Described by Nonlinear Parabolic Equations (Comments on paper No. 6 by Kolmogorov, Petrowsky and Piskunov) in I. G. Petrovsky's Collected Works in Differential Equations and Probability Theory, Akad. Nauk Moscow 1988, V. I. ARNOLD et al. Ed., pp. 333-358.

[Vo2] A.I. Vol'Pert, Wave Solutions of Parabolic Equations, Inst. Chemical Physics, Acad. Sci. (Chernogolovka), 1983, Russian preprint.

[VV1] A.I. Volpert and V.A. Volpert, Applications of the Rotation Theory of Vector Fields to the Study of Wave Solutions of Parabolic Equations, Trud. Moscow Math. Soc., Vol. 52, 1989. English. Translation: Trans. Moscow Math. Soc., Vol. 52, 1990, pp. 59-108. | Zbl

[VV2] A.I. Volpert and V.A. Volpert, Existence and Stability of Traveling Waves in Chemical Kinetics. Dynamics of Chemical and Biological Systems, Novosibirsk Nauka, 1989, pp. 56-131 (in Russian).

[VV3] A.I. Volpert and V.A. Volpert, Traveling Waves in Monotone Parabolic Systems, Preprint. Branch of the Inst. of Chemical Physics, Chernogolovka, 1990, 49 p. (in Russian).

[ZFK] J.B. Zeldovich and D.A. Frank-Kamenetskii, A Theory of Thermal Propagation of Flame, Acta Physiochimica U.R.S.S., Vol. 9, 1938. English Translation: In Dynamics of Curved Fronts, R. PELCÉ Ed., Perspectives in Physics Series, Academic Press, New York, 1988, pp. 131-140.