Skip to main content
SpringerLink
Log in

Cauchy problem for the essentially infinite-dimensional heat equation on a surface in a Hilbert space

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

It is proved that the Cauchy problem for a simple parabolic equation with essentially infinite-dimensional coefficients on bounded level surfaces of smooth functions in a Hilbert space is uniformly well posed.

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. Yu. V. Bogdanskii, “Cauchy problem for essentially infinite-dimensional parabolic equations on an infinite-dimensional sphere,”Ukr. Math. Zh.,35, No. 1, 18–22 (1983).

    Google Scholar 

  2. Yu. V. Bogdanskii, “Cauchy problem for the heat equation with an irregular elliptic operator,”Ukr. Mat. Zh.,41, No. 5, 584–590 (1989).

    Google Scholar 

  3. Yu. V. Bogdansky and Yu. L. Daletskii, “Cauchy problem for a simple parabolic equation with essentially infinite-dimensional elliptic operator,” in: Yu. L. Daletskii and S. V. Fomin,Measures and Differential Equations in Infinite-Dimensional Space, Supplement to Chapters IV–V, Kluwer AP, Dordrecht (1991), pp. 309–322.

    Google Scholar 

  4. Yu. V. Bogdanskii, “Dirichlet problem for the Poisson equation with essentially infinite-dimensional elliptic operator,”Ukr. Mat. Zh.,46, No. 7, 803–808 (1994).

    Google Scholar 

  5. Yu. V. Bogdanskii, “Cauchy problem for parabolic equations with essentially infinite-dimensional elliptic operators,”Ukr. Mat. Zh.,29, No. 6, 781–784 (1977).

    Google Scholar 

  6. J. A. Goldstein,Semigroups of Linear Operators and Applications, Oxford University Press, Oxford (1985).

    Google Scholar 

  7. Yu. L. Daletskii and S. V. Fomin,Measures and Differential Equations in Infinite-Dimensional Space, Kluwer AP, Dordrecht (1991).

    Google Scholar 

  8. Yu. L. Daletskii and M. G. Krein,Stability of Solutions of Differential Equations in Banach Spaces [in Russian], Nauka, Moscow (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kiev Polytechnic Institute, Kiev

    Yu. V. Bogdanskii

Authors
  1. Yu. V. Bogdanskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 6, pp. 737–746, June, 1995.

This work was supported by the Ukrainian State Committee on Science and Technology and (partially) by the International Science Foundation, Grant No. U44000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bogdanskii, Y.V. Cauchy problem for the essentially infinite-dimensional heat equation on a surface in a Hilbert space. Ukr Math J 47, 848–859 (1995). https://doi.org/10.1007/BF01058775

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01058775

Keywords

Search

Navigation