Archive for Rational Mechanics and Analysis

, Volume 111, Issue 1, pp 33–49 | Cite as

Multi-dimensional travelling-wave solutions of a flame propagation model

  • H. Berestycki
  • B. Larrouturou
  • P. L. Lions
Article

Keywords

Neural Network Complex System Propagation Model Nonlinear Dynamics Electromagnetism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S. Agmon, A. Douglis & L. Nirenberg, “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I”, Comm. Pure Appl. Math. 21, pp. 623–727 (1959).Google Scholar
  2. 2.
    F. Benkhaldoun & B. Larrouturou, “A finite-element adaptive investigation of curved stable and unstable flame fronts”, 76, pp. 119–134 (1989).Google Scholar
  3. 3.
    H. Berestycki & B. Larrouturou, “A semilinear elliptic equation in a strip arising in a two-dimensional flame propagation model”, J. für Reine und Angewandte Mathematik, 396, pp. 14–40 (1989).Google Scholar
  4. 4.
    H. Berestycki & B. Larrouturou, “Quelques aspects mathématiques de la propagation des flammes prémélangées”, Nonlinear partial differential equations and their applications, Collège de France seminar, Brezis & Lions, eds., Research Notes in Mathematics, Pitman-Longman, London, to appear.Google Scholar
  5. 5.
    H. Berestycki, B. Nicolaenko & B. Scheurer, “Travelling wave solutions to combustion models and their singular limits”, SIAM J. Math. Anal. 16 (6), pp. 1207–1242 (1985).Google Scholar
  6. 6.
    H. Berestycki & L. Nirenberg, “Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations”, J. Geom. and Phys. (special issue dedicated to I. M. Gelfand), to appear.Google Scholar
  7. 7.
    H. Berestycki & L. Nirenberg, “Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains, to appear.Google Scholar
  8. 8.
    R. Gardner, “Existence of multidimensional travelling wave solutions of an initialboundary value problem”, J. Diff. Equ. 61, pp. 335–379 (1986).Google Scholar
  9. 9.
    W. E. Johnson, “On a first-order boundary value problem for laminar flame theory”, Arch. Rational Mech. Anal. 13, pp. 46–54 (1963).Google Scholar
  10. 10.
    W. E. Johnson & W. Nachbar, “Laminar flame theory and the steady linear burning of a monopropellant”, Arch. Rational Mech. Anal. 12, pp. 58–91 (1963).Google Scholar
  11. 11.
    Ja. I. Kanel', “Stabilization of solutions of the Cauchy problem for equations encountered in combustion theory”, Mat. Sbornik 59, pp. 245–288 (1962).Google Scholar
  12. 12.
    Ja. I. Kanel', “On steady state solutions to systems of equations arising in combustion theory”, Dokl. Akad. Nauk USSR 149 (2), pp. 367–369 (1963).Google Scholar
  13. 13.
    B. Larrouturou, “Introduction to combustion modelling”, Springer Series in Computational Physics, to appear, (1990).Google Scholar
  14. 14.
    C. M. Li, Thesis, Courant Institute of Mathematical Sciences, New York-University, in preparation.Google Scholar
  15. 15.
    G. I. Sivashinsky, “Instabilities, pattern formation and turbulence in flames”, Ann. Rev. Fluid Mech. 15, pp. 179–199 (1983).Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • H. Berestycki
    • 1
    • 2
    • 3
  • B. Larrouturou
    • 1
    • 2
    • 3
  • P. L. Lions
    • 1
    • 2
    • 3
  1. 1.Laboratoire d'analyse numériqueUniversité Paris VIFrance
  2. 2.INRIA Sophia-Antipolis ValbonneFrance
  3. 3.CeremadeUniversité Paris IX DauphineFrance

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