Travelling fronts in cylinders
Annales de l'I.H.P. Analyse non linéaire, Volume 9 (1992) no. 5, p. 497-572
@article{AIHPC_1992__9_5_497_0,
     author = {Berestycki, Henri and Nirenberg, Louis},
     title = {Travelling fronts in cylinders},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {9},
     number = {5},
     year = {1992},
     pages = {497-572},
     zbl = {0799.35073},
     mrnumber = {1191008},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1992__9_5_497_0}
}
Berestycki, Henri; Nirenberg, Louis. Travelling fronts in cylinders. Annales de l'I.H.P. Analyse non linéaire, Volume 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 155203 | Zbl 0117.10001

[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 427837 | Zbl 0325.35050

[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 511740 | Zbl 0407.92014

[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 1044809 | Zbl 0702.35252

[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 988546 | Zbl 0658.35036

[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 1051478 | Zbl 0711.35066

[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 1145107 | Zbl 0763.76033

[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 807905 | Zbl 0596.76096

[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 1039342 | Zbl 0705.35004

[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 1110590 | Zbl 0780.35054

[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 1159383 | Zbl 0784.35025

[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 1205378 | Zbl 0840.35011

[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 480282 | Zbl 0338.35055

[Fi] P.C. Fife, Mathematical Aspects of Reacting and Diffusing Systems, Lect. Notes Biomath., No. 28, Springer-Verlag, New York, 1979. | MR 527914 | Zbl 0403.92004

[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 442480 | Zbl 0361.35035

[Fr1] M. Freidlin, Limit Theorems for Large Deviations and Reaction-Diffusion Equations, Ann. Prob., Vol. 13, 1985, pp. 639-675. | MR 799415 | Zbl 0576.60070

[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 829368 | Zbl 0549.35066

[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 145845 | Zbl 0111.40502

[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 157130 | Zbl 0152.10302

[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 0018.32106

[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 93706 | Zbl 0077.31501

[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 555661 | Zbl 0445.35063

[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 400428 | Zbl 0316.35053

[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 209618 | Zbl 0147.12303

[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 1145108

[R2] J.M. Roquejoffre, Convergence to Travelling Waves for Solutions of a Class of Semilinear Parabolic Equations (to appear). | MR 1270581 | Zbl 0806.35093

[Ve1] J.M. Vega, The Asymptotic Behavior of the Solutions of Some Semilinear Elliptic Equations in Cylindrical Domains, J. Diff. Eqs. (submitted). | Zbl 0803.35058

[Ve2] J.M. Vega, Travelling Wavefronts of Reaction-Diffusion Equations in Cylindrical Domains, Comm. P.D.E. (submitted). | Zbl 0816.35058

[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 0711.35064

[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.