Combined Parametrical and Transversal Excitation of a Stretched String in an Elastic Medium

2001 ◽  
Author(s):  
Caswita ◽  
A. H. P. van der Burgh
Keyword(s):  
Periodic Solutions ◽  
Elastic Medium ◽  
Integrodifferential Equation ◽  
Averaging Method ◽  
Telegraph Equation ◽  
Point Boundary ◽  
Time Periodic Solutions ◽  
The Stability ◽  
Two Parameters ◽  
Time Periodic

Abstract In this paper we consider a two-point boundary alue problem for an integrodifferential equation. This equation can be considered as a nonlinearly perturbed telegraph equation including both parametrical and transversal excitation. The attention will be focused on time-periodic solutions consisting of two modes. The first mode is generated by parametrical excitation and the second one is generated by vertical (transversal) excitation. This interaction of two modes can occur for special combinations of values of two parameters in the equation For the study of time-periodic solutions the averaging method will be used and the stability of the time-periodic solutions will be analyzed in linear approximation.

scholarly journals Bifurcation and stability of periodic solutions from a zero eigenvalue

1979 ◽  
Vol 21 (1) ◽  
pp. 2-20
Author(s):  
K. A. Landman
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
System Of Differential Equations ◽  
Double Zero ◽  
Zero Eigenvalue ◽  
Time Periodic Solutions ◽  
The Stability ◽  
Bifurcation And Stability ◽  
Time Periodic

AbstractA study is made of the branching of time periodic solutions of a system of differential equations in R2 in the case of a double zero eigenvalue. It is shown that the solution need not be unique and the period of the solution is large. The stability of these solutions is analysed. Examples are given and generalizations to larger systems are discussed.

On the time periodic thermistor problem

2004 ◽  
Vol 15 (1) ◽  
pp. 55-77 ◽  
Author(s):  
WALTER ALLEGRETTO ◽  
YANPING LIN ◽  
SHUQING MA
Keyword(s):  
Periodic Solutions ◽  
Degree Theory ◽  
Time Behaviour ◽  
Uniform Attractor ◽  
Long Time Behaviour ◽  
Galerkin Approximations ◽  
Long Time ◽  
Finite Dimensionality ◽  
Time Periodic Solutions ◽  
Time Periodic

In this paper we study a nonlocal parabolic/elliptic system which models thermistor behaviour in cases where heat losses to the surrounding gas play a significant role. The existence of time periodic solutions for the system is established through Faedo-Galerkin approximations and the Leray–Schauder degree theory. We show that for the small gas pressure case, the temperature of the time periodic solutions is positive. Moreover we consider the long time behaviour of the system and prove the existence of a uniform attractor. Finally, the finite dimensionality of the attractor is discussed.

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