The existence and uniqueness of solution of one coupled plate thermomechanics problem

• Autorzy: Krysko V. A. , Awrejcewicz J. , Bruk V. M.
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

thermo-elastic plate; vibrations; commutativity; hyperbolic equations; parabolic equations

PL

termo-elastyczne płyty; drgania; przemienność; równania hiperboliczne; równania paraboliczne

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2002
• Tom: Vol. 8, nr 1
• Strony: 129--139
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Krysko V. A.

• Technical University of Saratov, Department of Mathematics, 41005 Saratov, Russia

autor

Awrejcewicz J.

• Department of Automatics and Biomechanics Technical University of Lódź 1/15 Stefanowski St. 90-924 Lódź, Poland

autor

Bruk V. M.

• 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.