Preview

Fine Chemical Technologies

Advanced search

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

https://doi.org/10.32362/2410-6593-2017-12-3-81-86

Full Text:

Abstract

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.

About the Author

E. M. Kartashov
Moscow Technological University (Institute of Fine Chemical Technologies)
Russian Federation
Moscow 119571, Russia


References

1. Kartashov E.M. The method of integral transformations in the analytic theory of the thermal conductivity of solids // Izvestiya RAN. Energetika (Bulletine of RAS. Power Engineering). 1993. № 2. P. 99–127. (in Russ.).

2. Kartashov E.M. Calculation of temperature fields in solids based on improved convergence of FourierHankel series // Izvestiya RAN. Energetika (Bulletine of RAS. Power Engineering). 1993. № 3. P. 106–125. (in Russ.).

3. Kartashov E.M. Analytical methods in the theory of thermal conductivity of solids. M.: Vysshaya shkola Publ., 2001. 540 p. (in Russ.).

4. Koshlyakov N.S., Gliner E.B., Smirnov E.M. Equations in partial derivatives of mathematical physics. M.: Vysshaya shkola Publ., 1970. 710 p. (in Russ.).

5. Volkov I.K., Kanatnikov A.N. Integral transformations and operational calculus. M.: N.E. Bauman MGTU Publ., 1996. 228 p. (in Russ.).

6. Kartashov E.M., Kudinov V.A. Analytical theory of heat conductivity and applied thermoelasticity. M.: URSS Publ., 2012. 653 p. (in Russ.).

7. Kartashov E.M., Mikhailova N.A. Integral relations for analytic solutions of the generalized equation of nonstationary heat conductivity // Vestnik MITHT (Fine Chem. Technologies). 2011. V. 6. № 3. P. 106–110. (in Russ.).

8. Carslow G.G., Eger D. Thermal conductivity of solids. M.: Nauka Publ., 1964. 487 p. (in Russ.).

9. Sneddon I. Fourier transformations. Moscow: Publ. of Foreign Liter., 1955. 667 p. (in Russ.).


For citation:


Kartashov E.M. INTEGRAL TRANSFORMATION FOR THE THIRD BOUNDARY-VALUE PROBLEM OF NON-STATIONARY HEAT CONDUCTIVITY WITH A CONTINUOUS SPECTRUM OF EIGENVALUES. Fine Chemical Technologies. 2017;12(3):81-86. (In Russ.) https://doi.org/10.32362/2410-6593-2017-12-3-81-86

Views: 172


ISSN 2410-6593 (Print)
ISSN 2686-7575 (Online)