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On elliptic singular perturbation problems with several turning points

Part I: Theory of Singular Perturbations

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Part of the Lecture Notes in Mathematics book series (LNM,volume 942)

Keywords

  • Boundary Layer
  • Singular Point
  • Stochastic Differential Equation
  • Singular Perturbation
  • Singular Perturbation Problem

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References

  1. P.P.N. de Groen, Elliptic Singular Perturbations of First-Order Operators with Critical Points. Proc. Roy. Soc. Edinb. 74A, 7 (1974–75) pp. 91–113.

    MathSciNet  MATH  Google Scholar 

  2. W. Eckhaus, Matched Asymptotic Expansions and Singular Perturbations, North-Holland P.C., 1973.

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  3. S. Kamin, Elliptic perturbation of a first-order operator with a singular point of attracting type, Ind. Univ. Math. J. 27, 6 (1978), 935–952.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. S. Kamin, On singular perturbation problems with several turning points (in preparation).

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  5. Y. Kifer, The exit problem for small random perturbations of dynamical systems with a hyperbolic fixed point, Isr. J. Math. 40 (1981), 1, 74–96.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. N. Levinson, The first boundary value problem for εΔu+A(x,y)ux+B(x,y)uy+C(x,y)u=D(x,y) for small ε, Ann. of Math. (2) 51 (1950), 428–445.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. B.J. Matkowsky & Z. Schuss, The exit problem for randomly perturbed dynamical systems, SIAM J. Appl. Math. 33 (2), 1977, 365–382.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Z. Schuss, B. Matkowsky, The exit, problem: A new approach to diffusion across potential barriers, SIAM J. Appl. Math., 35, 3 (1979), 604–623.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Z. Schuss, Theory and applications of stochastic differential equations, J. Wiley & Sons, 1980.

    Google Scholar 

  10. A.D. Ventcel & M.I. Freidlin, On small perturbations of dynamical systems, Uspehi Mat. Nauk 25 (1970), no. 1 (151), 3–55; Russian Math. Surveys 25 (1970), no. 1, 1–56.

    MathSciNet  MATH  Google Scholar 

  11. M.I. Visik & L.A. Lyusternik, Regular degeneration and boundary layers for linear differential equations with a small parameter, Uspehi Mat. Nauk, 12 (1975), Amer. Mat. Soc. Translations Series 2, 20 (1972).

    Google Scholar 

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© 1982 Springer-Verlag

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Kamin, S. (1982). On elliptic singular perturbation problems with several turning points. In: Eckhaus, W., de Jager, E.M. (eds) Theory and Applications of Singular Perturbations. Lecture Notes in Mathematics, vol 942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094745

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  • DOI: https://doi.org/10.1007/BFb0094745

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11584-7

  • Online ISBN: 978-3-540-39332-0

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