| Title:
|
Bifurcation theory of the time-dependent von Kármán equations (English) |
| Author:
|
Brilla, Igor |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
29 |
| Issue:
|
1 |
| Year:
|
1984 |
| Pages:
|
3-13 |
| Summary lang:
|
English |
| Summary lang:
|
Slovak |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the author studies existence and bifurcation of a nonlinear homogeneous Volterra integral equation, which is derived as the first approximation for the solution of the time dependent generalization of the von Kármán equations. The last system serves as a model for stability (instability) of a thin rectangular visco-elastic plate whose two opposite edges are subjected to a constant loading which depends on the parameters of proportionality of this boundary loading. (English) |
| Keyword:
|
existence |
| Keyword:
|
bifurcation |
| Keyword:
|
nonlinear homogeneous Volterra integral equation |
| Keyword:
|
von Kármán equations |
| Keyword:
|
stability |
| Keyword:
|
rectangular visco-elastic plate |
| MSC:
|
45D05 |
| MSC:
|
45G10 |
| MSC:
|
45M10 |
| MSC:
|
73F15 |
| MSC:
|
73K10 |
| MSC:
|
74Hxx |
| idZBL:
|
Zbl 0538.45006 |
| idMR:
|
MR0729948 |
| DOI:
|
10.21136/AM.1984.104063 |
| . |
| Date available:
|
2008-05-20T18:23:48Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104063 |
| . |
| Reference:
|
[1] J. Brilla: Stability problems in mathematical theory of viscoelasticity.in Equadiff IV, Proceedings, Prague, August 22-26, 1977 (ed. J. Fabera). Springer, Berlin-Heidelberg- New York 1979. MR 0535322 |
| Reference:
|
[2] N. Distéfano: Nonlinear Processes in Engineering.Academic press, New York, London 1974. MR 0392042 |
| Reference:
|
[3] A. N. Kolmogorov S. V. Fomin: Elements of the theory of functions and functional analysis.(Russian). Izd. Nauka, Moskva 1976. MR 0435771 |
| Reference:
|
[4] J. L. Lions: Quelques méthodes de résolution des problèmes aux limites no linéaires.Dunod, Gautier-Villars, Paris 1969. MR 0259693 |
| Reference:
|
[5] F. G. Tricomi: Integral equations.Interscience Publishers, New York, 1957. Zbl 0078.09404, MR 0094665 |
| . |
