Advertisement

Differential Equations

, Volume 51, Issue 3, pp 376–390 | Cite as

On the existence of solutions of a nonlinear boundary value problem for the system of partial differential equations of the theory of Timoshenko type shallow shells with free edges

  • S. N. Timergaliev
Partial Differential Equations

Abstract

We study the solvability of a system of nonlinear second-order partial differential equations with given boundary conditions. The method is to reduce the original system to a single nonlinear differential equation, whose solvability is then proved with the use of the contraction mapping principle.

Keywords

Nonlinear Boundary Free Edge Hilbert Problem Nonlinear Integral Equation Shallow Shell 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Galimov, K.Z., Osnovy nelineinoi teorii tonkikh obolochek (Foundations of Nonlinear Theory of Thin Shells), Kazan, 1975.Google Scholar
  2. 2.
    Vorovich, I.I., Matematicheskie problemy nelineinoi teorii pologikh obolochek (Mathematical Problems in the Nonlinear Theory of Shallow Shells), Moscow: Nauka, 1989.Google Scholar
  3. 3.
    Karchevskii, M.M., Nonlinear Problems of the Theory of Plates and Shells and Their Difference Approximation, Izv. Vyssh. Uchebn. Zaved. Mat., 1985, no. 10, pp. 17–30.Google Scholar
  4. 4.
    Karchevskii, M.M., Solvability of Variational Problems in the Nonlinear Theory of Shallow Shells, Differ. Uravn., 1991, vol. 27, no. 7, pp. 1196–1203.MathSciNetGoogle Scholar
  5. 5.
    Timergaliev, S.N., The Bubnov-Galerkin Method for the Approximate Solution of Boundary Value Problems of the Nonlinear Theory of Thin Shells, Differ. Uravn., 2002, vol. 38, no. 12, pp. 1680–1689.MathSciNetGoogle Scholar
  6. 6.
    Timergaliev, S.N., Proof of the Solvability of a System of Partial Differential Equations in the Nonlinear Theory of Shallow Shells of Timoshenko Type, Differ. Uravn., 2012, vol. 48, no. 3, pp. 450–454.MathSciNetGoogle Scholar
  7. 7.
    Vekua, I.N., Obobshchennye analiticheskie funktsii (Generalized Analytic Functions), Moscow: Nauka, 1988.zbMATHGoogle Scholar
  8. 8.
    Gakhov, F.D., Kraevye zadachi (Boundary Value Problems), Moscow: Gosudarstv. Izdat. Fiz.-Mat. Lit., 1963.Google Scholar
  9. 9.
    Mikhailov, V.P., Differentsial’nye uravneniya v chastnykh proizvodnykh (Partial Differential Equations), Moscow: Nauka, 1976.Google Scholar
  10. 10.
    Krasnosel’skii, M.A., Topologicheskie metody v teorii nelineinykh integral’nykh uravnenii (Topological Methods in the Theory of Nonlinear Integral Equations), Moscow: Gosudarstv. Izdat. Tekhn.-Teor. Lit., 1956.Google Scholar
  11. 11.
    Duvaut, G. and Lions, J.-L., Inequalities in Mechanics and Physics, Berlin, 1976. Translated under the title Neravenstva v mekhanike i fizike, Moscow, 1980.CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Branch of Kazan Federal University in Naberezhnye ChelnyNaberezhnye ChelnyRussia

Personalised recommendations