Journal of Applied Analysis 08 (2002), No. 1, 129--140
Copyright Heldermann Verlag 2002
The Existence and Uniqueness of Solution of one Coupled Plate Thermomechanics Problem
Vadim A. Krysko
Dept. of Mathematics, Technical University, 41005 Saratov, Russia
Jan Awrejcewicz
Dept. of Automatics and Biomechanics, Technical University, 1/15 Stefanowski St., 90-924 Lódz, Poland
V. M. Bruk
Dept. of Mathematics, Technical University, 41005 Saratov, Russia
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).
Keywords: Thermo-elastic plate, hyperbolic and parabolic equations, vibrations, commutativity.
MSC: 35A07, 74K20; 35J15, 35L10
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