Skip to main content
SpringerLink
Log in

On the Dirichlet problem for quasi-linear elliptic equation with a small parameter

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper we deal with the Dirichlet problem for quasilinear elliptic equation with a small parameter at highest derivatives. In case the characteristics of the degenerated equation are curvilinear and the domain, where the problem is defined, is a bounded convex domain, we offer a method to construct the uniformly valid asymptotic solution of this problem, and prove that the solution of this problem really exists, and being uniquely determined as the small parameter is sufficiently small.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Berger, M. S., and Fraenkel, L. E., On the asymptotic solution of a nonlinear Dirichlet problem.J. Math. Mech. 19(7), (1978), 553–585.

    MathSciNet  Google Scholar 

  2. Fife, P. C., Semilinear elliptic boundary value problems with small parameters,Arch. Rat. Mech. and Anal., 52(2), (1973), 205–232.

    MATH  MathSciNet  Google Scholar 

  3. Roberts, P. H., Singularities of Hartmann layers,Proc. Royal Soc., Ser. A, 300 (1967), 91–107.

    Google Scholar 

  4. Grasman, J., On the birth of boundary layers,Math. Centre Tracts, 36,Amsterdam, (1971).

  5. Van Harten, A. J., Nonlinear singular perturbation problems: Proofs of correctness of a formal approximation based on a contraction principle in a Banach space.J. Math. Anal. and Appl., 65(1), (1978), 126–168.

    Article  MATH  MathSciNet  Google Scholar 

  6. Holland, C. J., Singular perturbations in elliptic boundary value problems,J. Diff. Equ., 20(1), (1976), 218–265.

    Article  MathSciNet  Google Scholar 

  7. Howes, F. A. Singularly perturbed semilinear elliptic boundary value problems,Comm.; Partial Diff. Equ., 4(1), (1979), 1–39.

    MATH  MathSciNet  Google Scholar 

  8. Леликов, Е.Ф, Об асимптоіике решеня эллитичещког уравния второго порядка с малым парамєтром при старших цроизводпых,Дифф, Урав., 12(10) (1976), 1852–1865.

    Google Scholar 

  9. Илъин, А. М., Калашников, А. С., Длейник, О. А., Линсйиые уравнения второго порядка лараболического типа,УМН., 17, 5(105), (1962), 3–146.

    Google Scholar 

  10. Ладыженская, О. А., Уралъцева, Н. Н., Линеинъе и Квазилинеинюс Уравневия Эллиптического Типа, Изд “Наука”, МосКва (1964).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fudan University, Shanghai

    Jiang Fu-ru

Authors
  1. Jiang Fu-ru
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fu-ru, J. On the Dirichlet problem for quasi-linear elliptic equation with a small parameter. Appl Math Mech 2, 25–50 (1981). https://doi.org/10.1007/BF02432051

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02432051

Keywords

Search

Navigation