Skip to main content
Log in

On a coupled system of abstract differential equations similar to the thermoelasticity equations

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

The study of a model system of differential equations arising from the dynamical problems of thermo elasticity is continued. The case of shifts of the general type is investigated. We employ the “commutant method” based on the properties of the operator Δ (A,B)=AB-BA.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. A. N. Botsenyuk and A. A. Pankov, “Coupled systems of abstract differential equations similar to the thermoelasticity equations,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 10, 6–8 (1982).

    Google Scholar 

  2. L. M. Gershtein, Yu. T. Sil'chenko, and P. E. Sobolevskii, “Semigroup approaches to the investigation of the problems of thermo elasticity,” in:Methods for the Study of Differential and Integral Operators [in Russian], Naukova Dumka, Kiev (1989), pp. 46–54.

    Google Scholar 

  3. L. M. Gershtein, “A coupled system of differential equations in a Banach space,”Ukr. Mat. Zh.,41, No. 7, 898–905 (1989).

    Google Scholar 

  4. F. G. Maksudov and K. Ya. Leonov, “On the solvability and uniqueness of a solution for a nonlinear mixed problem of thermoelasticity,”Dokl.Akad.Nauk SSSR,287, No. 6, 1310–1312(1986).

    Google Scholar 

  5. V. A. Karnaukhov,Coupled Thermoviscoelasticity Problems [in Russian], Naukova Dumka, Kiev (1970).

    Google Scholar 

  6. L. M. Gershtein and P. E. Sobolevskii, “A new approach to the study of solvability of evolutionary equations,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 10, 9–12 (1980).

    Google Scholar 

  7. L. M. Gershtein, “On the commutant method for the study of new classes of partial differential equations,” in:General Theory of Boundary Problems [in Russian], Naukova Dumka, Kiev (1983), p. 47.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Ukrainskii Matematicheskii Zhumal, Vol. 45, No. 8, pp. 1162–1165, August, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gershtein, L.M. On a coupled system of abstract differential equations similar to the thermoelasticity equations. Ukr Math J 45, 1297–1301 (1993). https://doi.org/10.1007/BF01070978

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01070978

Keywords

Navigation