| Title:
|
Explicit solution for Lamé and other PDE systems (English) |
| Author:
|
Rodionov, Alexei |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
51 |
| Issue:
|
6 |
| Year:
|
2006 |
| Pages:
|
583-595 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We provide a general series form solution for second-order linear PDE system with constant coefficients and prove a convergence theorem. The equations of three dimensional elastic equilibrium are solved as an example. Another convergence theorem is proved for this particular system. We also consider a possibility to represent solutions in a finite form as partial sums of the series with terms depending on several complex variables. (English) |
| Keyword:
|
systems of linear partial differential equations |
| Keyword:
|
constant coefficient |
| Keyword:
|
explicit solutions |
| Keyword:
|
several complex variables |
| Keyword:
|
elasticity |
| MSC:
|
32A99 |
| MSC:
|
34A05 |
| MSC:
|
35C10 |
| MSC:
|
35E20 |
| idZBL:
|
Zbl 1164.35332 |
| idMR:
|
MR2291783 |
| DOI:
|
10.1007/s10492-006-0022-x |
| . |
| Date available:
|
2009-09-22T18:27:31Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134654 |
| . |
| Reference:
|
[1] A. Rodionov: An interesting case of variables separation.Appl. Math. Lett. 13 (2000), 33–39. Zbl 0973.35049, MR 1760260, 10.1016/S0893-9659(00)00030-6 |
| Reference:
|
[2] V. Karachik: Polynomial solutions to systems of partial differential equations with constant coefficients.Yokohama Math. J. 47 (2000), 121–142. Zbl 0971.35014, MR 1763777 |
| Reference:
|
[3] P. S. Pedersen: A basis for polynomial solutions to systems of linear constant coefficient PDEs.Adv. Math. 117 (1996), 157–163. MR 1367588, 10.1006/aima.1996.0005 |
| Reference:
|
[4] E. S. Cheb-Terrab, K. Von Bülow: A computational approach for the analytical solving of partial differential equations.Comput. Phys. Commun. 90 (1995), 102–116. 10.1016/0010-4655(95)00083-R |
| Reference:
|
[5] A. I. Aleksandrovic: Applying the theory of functions of two complex variables to the theory of elasticity.Sov. Phys., Dokl. 22 (1977), 48–50. Zbl 0375.73018 |
| . |
