Skip to main content
Springer Nature Link
Log in

The cauchy problem of a degenerate parabolic equation

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

This note is concerned with the existence of a weak solution for a degenerate Cauchy problem of parabolic type in then-dimensional spaceR n. The degenerate property is in the sense that the matrix (a ij(t,x)) involved in the differential operator is not necessarily positive definite. The essential idea is the construction of a suitable function spaceH and to prove the existence of a weak solution inH.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Ivanov, A. V.: A boundary-value problem for degenerate second order parabolic linear equations (Russian). Zap. Naucn. Sem. Leningrad Otdel. Mat. Inst. Steklov.14, 48–88 (1969).

    Google Scholar 

  2. Lions, J. L.: Equations Différentielles Opérationelles. Berlin-Göttingen-Heidelberg: Springer. 1961.

    Google Scholar 

  3. Matsuzawa, T.: On some degenerate parabolic equations I, II. Nagoya Math. J.51, 57–77 (1973) and52, 61–84 (1973).

    Google Scholar 

  4. Oleinnik, O. A.: On the smoothness of the solutions of degenerate elliptic and parabolic equations. Sov. Math. Dokl.6, 972–976 (1965).

    Google Scholar 

  5. Pao, C. V.: On a non-uniform parabolic equation with mixed boundary condition. Proc. Amer. Math. Soc.49, 83–89 (1975).

    Google Scholar 

  6. Yoshida, K.: Functional Analysis. Berlin-Heidelberg-New York: Springer. 1966.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, North Carolina State University, 27607, Raleigh, NC, USA

    C. V. Pao

Authors
  1. C. V. Pao
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pao, C.V. The cauchy problem of a degenerate parabolic equation. Monatshefte für Mathematik 83, 201–205 (1977). https://doi.org/10.1007/BF01541636

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01541636

Keywords