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Green functions and periodic solution to the m-parabolic equation with boundary-value conditions of Riquier type

100%

Barański F. , Zdankiewicz Z.

tom Nr 32

5-13

The subject of the paper is the construction of the periodic solutions to the w-caloric equation P"'u(x,t) = 0, P=D(2)*(2)-D, P(2) =P(P), Pm = P(P(m~l) in the strip (mathemical formula), satisfying the periodic boundary-value conditions (mathematical formula), where h(11)(t), h1,2(t) are the periodic functions with the period p > 0.

Modelling and Investigation of Temperature Influence on Normal Mode of the Layer Oscillations

86%

Nahirnyj T. , Tchervinka K.

tom Vol. 21

279--282

In this paper the boundary value problems for local gradient body are formulated and investigated. Using averaging over oscillation period operation there is obtained the set of differential equations for determining the averaged and wave components of thermo-elastic fields. The methods for approximate integration of this set are proposed (using expansion over the small parameter of the problem). The normal mode layer oscillations are studied for various mechanical conditions at the layer surfaces (fixed surfaces, one surface is fixed, both surfaces are free). The analysis of equations for normal mode frequency is carried out. The frequencies dependences on temperature and parameters being characteristics of interface nonhomogeneity are studied.