Open AccessINTEGRAL TRANSFORMATION FOR THE THIRD BOUNDARY-VALUE PROBLEM OF NON-STATIONARY HEAT CONDUCTIVITY WITH A CONTINUOUS SPECTRUM OF EIGENVALUES
Author(s) -
Э. М. Карташов
Publication year - 2017
Publication title -
tonkie himičeskie tehnologii
Language(s) - English
Resource type - Journals
eISSN - 2686-7575
pISSN - 2410-6593
DOI - 10.32362/2410-6593-2017-12-3-81-86
Subject(s) - mathematics , boundary value problem , mathematical analysis , mixed boundary condition , free boundary problem , elliptic boundary value problem , robin boundary condition , eigenvalues and eigenvectors , dirichlet boundary condition , neumann boundary condition , cauchy boundary condition , physics , quantum mechanics
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.