Skip to main content
Log in

On an approach to the construction of a solution of the generalized coupling problem

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

We propose a method of solving generalized coupling problems by reducing them to an inhomogeneous differential equation in the space of generalized functions that can be solved using a normalized fundamental function or a Green's function.

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.

Similar content being viewed by others

Literature cited

  1. G. Bremerman,Distributions, Complex Variables, and Fourier Transforms, Addison-Wesley, Reading, Massachusetts (1965).

    Google Scholar 

  2. V. S. Vladimirov,Generalized Functions in Mathematical Physics [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  3. M. M. Drin' and S. D. Ivasishen, “The Green's matrix of a general boundary-value problem for a Petrovskii-parabolic system with discontinuous coefficients,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 11, 7–10 (1984).

    Google Scholar 

  4. N. V. Zhitarashu, “On the well-posed solvability in generalized functions of a class of nonlocal parabolic boundary-value problems and coupling problems,”Izv. Akad. Nauk Mold. SSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 3, 12–16 (1986).

    Google Scholar 

  5. Yu. M. Kolyano, A. N. Kulik, and R. M. Kushnir, “On the statement of a generalized coupling problem for the equations of thermoelasticity of piecewise homogeneous bodies,”Dokl. Akad. Nauk Ukr. SSR, Ser. A., No. 2, 43–47 (1980).

    Google Scholar 

  6. R. M. Kushnir, “On the solution of problems of thermoelasticity for piecewise homogeneous bodies by application of generalized functions,” in:Proceedings of the Ninth Conference of Young Scholars of the Institute for Applied Problems of Mechanics and Mathematics of the Ukrainian Academy of Sciences [in Russian], L'vov (1983), Pt. 1, pp. 109–113.

  7. R. M. Kushnir, “On the construction of solutions of ordinary linear differential equations with piecewise-constant coefficients,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 9, 54–57 (1980).

    Google Scholar 

  8. R. M. Kushnir and A. K. Prikarpats'kii, “Conditions for existence of fundamental solutions of ordinary differential equations in the class of generalized functions,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 9, 23–25 (1987).

    Google Scholar 

  9. G. P. Lopushanskaya, “On some properties of the solutions of nonlocal elliptic problems in the space of generalized functions,”Ukr. Mat. Zh.,41, No. 11, 1487–1494 (1989).

    Google Scholar 

  10. G. P. Lopushanskaya, “On the solution of certain classes of inverse boundary-value problems in the space of distributions,” Preprint, UkrNIINTI, No. 48-Uk90.

  11. G. P. Lopushans'ka, “On a method of solving boundary-value problems in spaces of distributions,”Visnik L'viv Univ., Ser. Mekh.-Mat., No. 36, 28–33 (1991).

    Google Scholar 

  12. V. E. Lyantse, D. E. Potyagailo, and M. O. Fedik, “On the coupling boundary-value problem,”Mat. Met. i Fiz.-Mekh. Polya, No. 30, 20–24 (1989).

    Google Scholar 

  13. V. A. Osadchuk and S. Ya. Oliinik, “A system of initial equations of elastic equilibrium of piecewise homogeneous shells with proper stresses,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 10, 30–33 (1986).

    Google Scholar 

  14. Ya. S. Podstrigach, V. A. Lomakin, and Yu. M. Kolyano,Thermoelasticity of Bodies of Inhomogeneous Structure [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  15. Y. A. Roitberg and Z. G. Sheftel', “Green's formula and conditions for solvability of nonlocal elliptic boundary-value problems,”Ukr. Mat. Zh.,25, No. 4, 475–487 (1973).

    Google Scholar 

  16. M. F. Stasyuk, “The structure of solutions of ordinary and quasidifferential equations with piecewise-variable coefficients,”Dop. Akad. Nauk Ukr. RSR, Ser. A, No. 12, 31–35 (1982).

    Google Scholar 

Download references

Authors

Additional information

Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 198–203.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kushnir, R.M., Lopushans'ka, G.P. On an approach to the construction of a solution of the generalized coupling problem. J Math Sci 67, 3012–3017 (1993). https://doi.org/10.1007/BF01095888

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01095888

Keywords

Navigation