INTEGRAL TRANSFORMATION FOR THE THIRD BOUNDARY-VALUE PROBLEM OF NON-STATIONARY HEAT CONDUCTIVITY WITH A CONTINUOUS SPECTRUM OF EIGENVALUES

The mathematical theory of constructing an integral transformation and the inversion formula for it for the third boundary value problem in a domain with a continuous spectrum of eigenvalues are developed. The method is based on the operational solution of the initial problem with an initial function of general form satisfying the Dirichlet condition and a homogeneous boundary condition of the third kind. On the basis of the obtained relations, a series of analytical solutions of the third boundary value problem for a parabolic equation in various equivalent functional forms is proposed. An integral representation of the analytic solutions of the third boundary-value problem is proposed for the general form of the representation of boundary-value functions in the initial formulation of the problem. The corresponding Green's function is written out.

the third boundary value problem, semi-bounded domain, integral transformation, formula of treatment, analytical solutions

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