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Abstrakty
The thermo-elastic plate system of equations is analysed. The sufficient conditions of existence, uniqueness and continuity dependence on initial data of the Cauchy problem solutions for differential-operational equation of mixed type (a part of the equation of hyperbolic type, and a part of parabolic type) are given in this paper. If the operational coefficients are suitably chosen, the investigated equation can be used to obtain a differential equation describing vibrations of a plate — the modified Germain-Lagrange equation of hyperbolic type. Moreover, in order to define the temperature field, one can use a three-dimensional equation of thermal conductivity (a parabolic equation).
Wydawca
Czasopismo
Rocznik
Tom
Strony
129--139
Opis fizyczny
Bibliogr. 6 poz.
Twórcy
autor
- Technical University of Saratov, Department of Mathematics, 41005 Saratov, Russia
autor
- Department of Automatics and Biomechanics Technical University of Lódź 1/15 Stefanowski St. 90-924 Lódź, Poland
autor
- Technical University of Saratov, Department of Mathematics, 41005 Saratov, Russia
Bibliografia
- [1] Awrejcewicz, J., Krysko, V. A., Numerical Analysis of Shells with Thermal Load (in Polish), Scientific-Technical Publisher WNT, Warsaw, 1998.
- [2] Berezanskij, Yu. M., Expansions in Eigenfunctions of Self-Adjoint Operators (in Russian), Naukova Dumka, Kiev, 1965, Amer. Math. Soc. Transi. Ser. 2 17, Providence, RI, 1968.
- [3] Krein, S. G., Linear Differential Equations in Banach Spaces (in Russian), Nauka, Moskva, 1967.
- [4] Lasiecka, I., Finite dimensionality and compactness of attractor for von Kármán equations with nonlinear dissipation, Nonlinear Differential Equations Appl. 6 (1999), 337-472.
- [5] Riesz, F., Szökefalvi-Nagy, B., Lectures on Functional Analysis, Undaw, New York,
- [6] Triggiani, R., Improvent of stability properties of hyperbolic damped wave equation via boundary feedback, Lecture Notes in Control and Inform. Sci. 75 (1985), Springer, Berlin, 400-409.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0014-0008