# Bifurcation theory of the time-dependent von Kármán equations

Aplikace matematiky (1984)

- Volume: 29, Issue: 1, page 3-13
- ISSN: 0862-7940

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topBrilla, Igor. "Bifurcation theory of the time-dependent von Kármán equations." Aplikace matematiky 29.1 (1984): 3-13. <http://eudml.org/doc/15328>.

@article{Brilla1984,

abstract = {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.},

author = {Brilla, Igor},

journal = {Aplikace matematiky},

keywords = {existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate; existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate},

language = {eng},

number = {1},

pages = {3-13},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Bifurcation theory of the time-dependent von Kármán equations},

url = {http://eudml.org/doc/15328},

volume = {29},

year = {1984},

}

TY - JOUR

AU - Brilla, Igor

TI - Bifurcation theory of the time-dependent von Kármán equations

JO - Aplikace matematiky

PY - 1984

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 29

IS - 1

SP - 3

EP - 13

AB - 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.

LA - eng

KW - existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate; existence; bifurcation; nonlinear homogeneous Volterra integral equation; von Kármán equations; stability; rectangular visco-elastic plate

UR - http://eudml.org/doc/15328

ER -

## References

top- 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. (1977) MR0535322
- N. Distéfano, Nonlinear Processes in Engineering, Academic press, New York, London 1974. (1974) MR0392042
- A. N. Kolmogorov S. V. Fomin, Elements of the theory of functions and functional analysis, (Russian). Izd. Nauka, Moskva 1976. (1976) MR0435771
- J. L. Lions, Quelques méthodes de résolution des problèmes aux limites no linéaires, Dunod, Gautier-Villars, Paris 1969. (1969) MR0259693
- F. G. Tricomi, Integral equations, Interscience Publishers, New York, 1957. (1957) Zbl0078.09404MR0094665

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