Hybrid Legendre-Fourier integral transforms on the polar axis. (Russian) Zbl 0712.44004
The author considers the solutions of a pair of partial differential equations of parabolic type in the domains \(\{\) (t,r), \(t>0\), \(r\in (0,R)\}\) and \(\{\) (t,r), \(t>0\), \(r\in (R,\infty)\}\), respectively, under initial value conditions with respect to t and transition conditions at \(r=R\). This leads to a continuous integral transformation with Legendre functions in the kernel, which is of index type.
Reviewer: H.-J.Glaeske
MSC:
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 35K50 | Systems of parabolic equations, boundary value problems (MSC2000) |
