| Title:
|
On the solution of some non-local problems (English) |
| Author:
|
Criado, F. |
| Author:
|
Criado, F., Jr. |
| Author:
|
Odishelidze, N. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
2 |
| Year:
|
2004 |
| Pages:
|
487-498 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with two types of non-local problems for the Poisson equation in the disc. The first of them deals with the situation when the function value on the circle is given as a combination of unknown function values in the disc. The other type deals with the situation when a combination of the value of the function and its derivative by radius on the circle are given as a combination of unknown function values in the disc. The existence and uniqueness of the classical solution of these problems is proved. The solutions are constructed in an explicit form. (English) |
| Keyword:
|
non-local problem |
| Keyword:
|
Poisson equation |
| Keyword:
|
discrete Fourier transform |
| MSC:
|
35J05 |
| MSC:
|
35J25 |
| idZBL:
|
Zbl 1080.35015 |
| idMR:
|
MR2059268 |
| . |
| Date available:
|
2009-09-24T11:14:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127905 |
| . |
| Reference:
|
[1] A. Bitsadze and A. Samarski: On some simplest generalizations of linear elliptic problems.Dokl. Akad. Nauk SSSR 185 (1969), 739–740. (Russian) MR 0247271 |
| Reference:
|
[2] A. Bitsadze: Boundary Value Problems for Elliptic Equations of Second Order.Nauka, Moscow, 1986. (Russian) |
| Reference:
|
[3] D. Gordeziani: On solvability of some boundary value problems for one variant of equations of thin shells.Dokl. Akad. Nauk SSSR 215 (1974), 1289–1292. (Russian) MR 0391657 |
| Reference:
|
[4] D. Gordeziani and T. Z. Djioev: The generalization of Bitsadze-Samarski problem with reference to the problems of baroclinic sea dynamics.Outlines on Physics and Chemistry of Waters of the Black Sea, IO ANSSSR, Moscow, 1978. (Russian) |
| Reference:
|
[5] U. Dini: Sulla integrazione della equazione $\Delta ^{2}u=0$.Brioschi Ann. VI (1873), 305–345. (Italian) |
| Reference:
|
[6] E. Obolashvili: Solution of nonlocal problems in plane elasticity theory.Current Problems of Mathematical Physics, Vol. 2. Transactions of All-Union Symposium, Gos. Univ., Tbilisi, 1987, pp. 295–302, 394. (Russian) MR 0991842 |
| Reference:
|
[7] E. Obolashvili: Nonlocal problems for some partial differential equations.Complex Variables Theory Appl. 19 (1992), 71–79. Zbl 0779.35019, MR 1228330, 10.1080/17476939208814560 |
| Reference:
|
[8] E. Obolashvili: P.D.E. in Clifford Analysis.Longman, Addison Wesley, 1998. MR 1697655 |
| Reference:
|
[9] O. Sjöstrand: Sur une equation aux derivées partielles due type composite.Ark. Mat. Astron. Fys. 25A (1937), no. 21, 1–11. |
| . |
