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1 Journal of Applied Analysis

1 2002

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

Krysko V. A., Awrejcewicz J., Bruk V. M.

Journal of Applied Analysis

2002

Vol. 8, nr 1

129-139

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).