Advertisement

Evolution Equations with Boundary Layers

Chapter
  • 1.8k Downloads
Part of the Texts in Applied Mathematics book series (TAM, volume 50)

Keywords

Boundary Layer Evolution Equation Neumann Condition Riemann Function Slow Manifold 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

9.7 Guide to the Literature

  1. 5.
    Aris, R. (1975), The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, 2 vols., Oxford University Press, Oxford.Google Scholar
  2. 21.
    Buckmaster, J.D. and Ludford, G.S.S. (1983), Lectures on mathematical combustion, CBSM-NSF Conf. Appl. Math. 43, SIAM, Philadelphia.Google Scholar
  3. 24.
    Butuzov, V.F. and Vasiléva, A.B. (1983), Singularly perturbed differential equations of parabolic type, in Asymptotic Analysis II, Lecture Notes in Mathematics 985 (Verhulst, F., ed.) Springer, Berlin, pp. 38–75.CrossRefGoogle Scholar
  4. 32.
    Class, A.G., Matkowsky, B.J., and Klimenko, A.Y. (2003), A unified model of flames as gasdynamic discontinuities, J. Fluid Mech. 491, pp. 11–49.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 36.
    de Jager, E.M. and Jiang Furu (1996), The Theory of Singular Perturbations, Elsevier, North-Holland Series in Applied Mathematics and Mechanics 42, Amsterdam.Google Scholar
  6. 47.
    Eckhaus, W. and Garbey, M. (1990), Asymptotic analysis on large timescales for singular perturbations of hyperbolic type, SIAM J. Math. Anal. 21, pp. 867–883.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 58.
    Fife, P.C. (1988), Dynamics of Internal Layers and Diffusive Interfaces, CBSM-NSF Conf. Appl. Math. 53, SIAM, Philadelphia.Google Scholar
  8. 63.
    Geel, R. (1981), Linear initial value problems with a singular perturbation of hyperbolic type, Proc. R. Soc. Edinburgh Section (A) 87, pp. 167–187 and 89, pp. 333–345.zbMATHMathSciNetGoogle Scholar
  9. 82.
    Holmes, M.H. (1998), Introduction to Perturbation Methods, Texts in Applied Mathematics 20, Springer-Verlag, New York.Google Scholar
  10. 95.
    Jones, C.K.R.T. (1994), Geometric singular perturbation theory, in Dynamical Systems, Montecatini Terme 1994 (Johnson, R., ed.), Lecture Notes in Mathematics 1609, pp. 44–118, Springer-Verlag, Berlin.CrossRefGoogle Scholar
  11. 98.
    Kaper, T.J. (1999), An introduction to geometric methods and dynamical systems theory for singular perturbation problems, in Proceedings Symposia Applied Mathematics 56: Analyzing Multiscale Phenomena Using Singular Perturbation Methods, (Cronin, J. and O’Malley, Jr., R.E., eds.). pp. 85–131, American Mathematical Society, Providence, RI.Google Scholar
  12. 99.
    Kaper, T.J. and Jones, C.K.R.T. (2001), A primer on the exchange lemma for fast-slow systems, IMA Volumes in Mathematics and its Applications 122: Multiple-Time-Scale Dynamical Systems, (Jones, C.K.R.T., and Khibnik, A.I., eds.). Springer-Verlag, New York.Google Scholar
  13. 104.
    Kevorkian, J.K. and Cole, J.D. (1996), Multiple Scale and Singular Perturbation Methods, Springer-Verlag, New York.zbMATHGoogle Scholar
  14. 131.
    Matkowsky, B.J. and Sivashinsky, G.I. (1979), An asymptotic derivation of two models in flame theory associated with the constant density approximation, SIAM J. Appl. Math. 37, pp. 686–699.zbMATHCrossRefMathSciNetGoogle Scholar
  15. 168.
    Shih, S.-D. and R.B. Kellogg (1987), Asymptotic analysis of a singular perturbation problem, SIAM J. Math. Anal. 18, pp. 1467–1511.zbMATHCrossRefMathSciNetGoogle Scholar
  16. 169.
    Shih, S.-D. (2001), On a class of singularly perturbed parabolic equations, Z. Angew. Math. Mech. 81, pp. 337–345.zbMATHCrossRefGoogle Scholar
  17. 179.
    Szmolyan, P. (1992), Analysis of a singularly perturbed traveling wave problem, SIAM J. Appl. Math. 52, pp. 485–493.zbMATHCrossRefMathSciNetGoogle Scholar
  18. 198.
    Van Harten, A. (1979), Feed-back control of singularly perturbed heating problems, in Lecture Notes in Mathematics 711 (Verhulst, F., ed.), Springer-Verlag, Berlin, pp. 94–124.Google Scholar
  19. 199.
    Van Harten, A. (1982), Applications of singular perturbation techniques to combustion theory, in Lecture Notes in Mathematics 942 (Eckhaus, W., and de Jager, E.M., eds.), Springer-Verlag, Berlin, pp. 295–308.CrossRefGoogle Scholar
  20. 205.
    Vasil’eva, A.B., Butuzov, V.F. and Kalachev, L.V. (1995), The Boundary Function Method for Singular Perturbation Problems, SIAM Studies in Applied Mathematics 14, SIAM, Philadeplhia.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Personalised recommendations