Abstract
Traveling waves in inert or reactive flows can be classified into deflagration waves and detonation waves [Wil85]. The structure of reactive exothermic detonation waves will not be addressed in this book and we refer the reader to [Wil85]. On the other hand, in the context of combustion phenomena, weak deflagration waves typically correspond to plane flames and have been the object of intensive mathematical, physical, chemical, and asymptotic investigations over the last decade [Wil85].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. P. Aldushin, Ya. B. Zeldovitch, and S. I. Khudyaev, Numerical Investigation of the Flame Propagation in a Mixture Reacting at the Initial Temperature, Fiz. Goreniya Vzryva (Comb. Explos. Shock Waves), 15, (1979), pp. 20–27.
J. Bebernes and D. Eberly, Mathematical Problems from Combustion Theory, Springer-Verlag, New York, (1989).
A. Ben-Israel and T. N. E. Greville, Generalized Inverses, Theory and Applications, John Wiley & Sons, Inc., New York, (1974).
H. Berestycki and B. Larrouturou, Sur les Modèles de Flammes en Chimie Complexe, C. R. Acad. Sci. Paris, Série I, 317, (1993), pp. 173–176.
A. Bonnet, Travelling Wave for Planar Flames with Complex Chemistry Reaction Network, Comm. Pure Appl. Math., XLV, (1992), pp. 1271–1302.
A. Bonnet, Contribution à l’Étude des Problèmes Elliptiques et à la Modélisation Mathématique de la Combustion, Mémoire d’Habilitation à Diriger des Recherches, Université Paris 6, (1994).
N. Bourbaki, Fonctions d’une Variable Réelle, Éléments de Mathématiques, Diffusion C. C. L. S., (1976).
J. D. Buckmaster and G. S. S. Ludford, Theory of Laminar Flames, Cambridge University Press, Cambridge, (1982).
P. Clavin, Dynamic Behavior of Premixed Flame Fronts in Laminar and Turbulent Flows, Prog. Ener. Comb. Sci., 11, (1985), pp. 1–59.
K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, (1988).
V. Giovangigli, An Existence Theorem for a Free-Boundary Problem of Hypersonic Flow Theory, SIAM J. Math. Anal., 24, (1993), pp. 571–582.
V. Giovangigli, Plane Flames with Multicomponent Transport and Complex Chemistry, Internal Report, 366, Centre de Mathématiques Appliquées de l’Ecole Polytechnique, (1997).
V. Giovangigli, Flames Planes avec Transport Multi-espece et Chimie Complexe, C. R. Acad. Sci. Paris, 326, Série I, (1998), pp. 775–780.
V. Giovangigli, Plane Flames with Multicomponent Transport and Complex Chemistry, Math. Mod. Meth. Appl. Sci., 9, (1999), pp. 337–378.
V. Giovangigli and M. Smooke, Application of Continuation Techniques to Plane Premixed Laminar Flames, Comb. Sci. Tech., 87, (1992), pp. 241–256.
S. Heinze, Travelling Waves in Combustion Processes with Complex Chemical Networks, Trans. Amer. Soc., 304, (1987), pp. 405–416.
J. O. Hirschfelder, C. F. Curtiss, and D. E. Campbell, The Theory of Flames and Detonations, Fourth International Symposium on Combustion, (1953), pp. 190–210.
J. Leray and J. Schauder, Topologie et Equations Fonctionnelles, Ann. Sci. École Norm. Sup., 51, (1934), pp. 45–78.
A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Appl. Math. Sci., 53, Springer-Verlag, New-York, (1984).
J. Quinard, G. Searby, and L. Boyer, Cellular Structures on Premized Flames in a Uniform Laminar Flow, Lect. Notes Phys., 210, Springer-Verlag, Berlin, (1984), pp. 331–341.
M. Sermange, Mathematical and Numerical Aspects of One-Dimensional Laminar Flame Simulation, Appl. Math. Opt., 14, (1986), pp. 131–153.
J. M. Roquejoffre, Étude Mathématique d’un Modèle de Flamme Plane, C. R. Acad. Sci. Paris, 311, Série I, (1990), pp. 593–596.
J. M. Roquejoffre and J. P. Vila, Stability of ZND Detonation Waves in the Majda Combustion Model, Preprint, (1998.
J. T. Schwartz, Nonlinear Functional Analysis, Gordon and Breach, New York, (1969).
A. Vol’pert and S Hudjaev, Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics, Mechanics: Analysis 8, Martinus Nijhoff Publishers, Dordrecht, (1985).
V. A. Volpert and V. A. Volpert, Travelling Wave Solutions of Monotone Parabolic Systems, Preprint, Inst. Chem. Phys., Chernogolovka, (in Russian), (1990), (Also, Preprint 146, Université de Lyon 1, 1993).
A. I. Volpert, V. A. Volpert, and V. A. Volpert, Travelling Wave Solutions of Parabolic Systems, Trans. Math. Mono., AMS, 140, (1994).
F. A. Williams, Combustion Theory, Second ed., The Benjamin/Cummings Publishing Company, Inc., Menlo Park, (1985).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Giovangigli, V. (1999). Anchored Waves. In: Multicomponent Flow Modeling. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1580-6_11
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1580-6_11
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7202-1
Online ISBN: 978-1-4612-1580-6
eBook Packages: Springer Book Archive