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 functio...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | Russian |
| Published: |
MIREA - Russian Technological University
2017-06-01
|
| Series: | Тонкие химические технологии |
| Subjects: | |
| Online Access: | https://www.finechem-mirea.ru/jour/article/view/97 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 2410-6593 2686-7575 |