Skip to main content

Singularly perturbed differential equations of parabolic type

Part 1 Survey Paper

Part of the Lecture Notes in Mathematics book series (LNM,volume 985)

Keywords

  • Boundary Layer
  • Periodic Solution
  • Corner Point
  • Supplementary Condition
  • Exponential Estimate

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Tikhonov, A.N., Systems of differential equations containing small parameters multiplying some of the derivatives, Mat. Sb. 31, 73 (1952), 575–586, (in Russian).

    Google Scholar 

  2. Vasil’eva, A.B. and Butuzov, V.F., Asymptotic expansions of solutions of singularly perturbed equations, Nauka, Moscow (1973), (in Russian).

    MATH  Google Scholar 

  3. Butuzov, V.F. and Nesterov, A.V., On a singularly perturbed equation of parabolic type, Vestnik Moscow Univ., Vyčisl. Matem. i Kibernetika 2 (1978) (in Russian).

    Google Scholar 

  4. Butuzov, V.F., Asymptotics of solutions of some model problems in chemical kinetics taking diffusion into account, Dokl. Akad. Nauk 242, 2 (1978), transl. Soviet Math. Dokl. 242, 1079–1083 (1978).

    MathSciNet  MATH  Google Scholar 

  5. Butuzov, V.F., Corner boundary layers in singularly perturbed partial differential equations, Diff. Urav. 15, 10, 1848 (1979), transl. Diff. Equations 15, 10, 1318–1327 (1979)

    MathSciNet  MATH  Google Scholar 

  6. Butuzov, V.F. and Nesterov, A.V., On the asymptotics of the solution of an equation of parabolic type with small parameters multiplying the highest derivatives, Z. Vyčisl. Matem. i. Matem. Piz. 22, 4 (1982), to be transl. in USSR Comput. Maths. Math. Phys.

    MathSciNet  Google Scholar 

  7. Smirnov, V.I., A course in higher mathematics, part 4, Nauka, Moscow (1974) (in Russian).

    Google Scholar 

  8. Vasil’eva, A.B. and Butuzov, V.F., Singularly perturbed equations in the critical case, Moscow Izd. MGU (1978), transl. by F. Howes, MRC Techn. Summ. Report 2039 (1980).

    Google Scholar 

  9. Romanovskii, Yu.M., Stepanova, N.V. and Černavskii, D.S., Mathematical modelling in biophysics, Nauka, Moscow (1975) (in Russian).

    Google Scholar 

  10. Dvoryanov, S.V., A periodic solution of a singularly perturbed autonomous parabolic system, Diff. Urav. 16, 9, 1617, transl. Diff. Equations 16, 9, 1040–1044.

    Google Scholar 

  11. Mitropol’skii, Yu.A., The method of averaging in nonlinear mechanics, Naukova dumka, Kiev (1971) (in Russian).

    Google Scholar 

  12. Vasil’eva, A.B. and Tupčiev, V.A., Periodic nearly-discontinuous solutions of systems of differential equations with a small parameter in the derivatives, Dokl. Akad. Nauk, 178, 4 (1968), transl. Soviet Math. Dokl. 9, 1, 179–183 (1968).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1983 Springer-Verlag

About this paper

Cite this paper

Butuzov, V.F., Vasil’eva, A.B. (1983). Singularly perturbed differential equations of parabolic type. In: Verhulst, F. (eds) Asymptotic Analysis II —. Lecture Notes in Mathematics, vol 985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062362

Download citation

  • DOI: https://doi.org/10.1007/BFb0062362

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12286-9

  • Online ISBN: 978-3-540-39612-3

  • eBook Packages: Springer Book Archive