We consider semilinear evolution equations of the form a(t)∂ttu+ b(t)∂tu + Lu = f(x, u) and b(t)∂tu + Lu = f(x, u), with possibly unbounded a(t) and possibly sign-changing damping coefficient b(t), and determine precise conditions for which linear instability of the steady state solutions implies nonlinear instability. More specifically, we prove that linear instability with an eigenfunction of...

A Hadamard instability analysis of the partial differential equations governing a coupled thermo-mechano-chemical system predicts instability of the spinoidal decomposition type as well as instability of the "negative creep" type.

This paper deals with dynamic Stability of single walled carbon nanotube. Strain gradient theory and Euler-Bernouli beam theory are implemented to investigate the dynamic stability of SWCNT embedded in an elastic medium. The equations of motion were derived by Hamilton principle and non-local elasticity approach. The nonlocal parameter accounts for the small-size effects when dealing with nano-...

prediction of fluid-elastic instability is a great matter of importance in designing cross-flow tube bundles from the perspective of vibration. in the present paper, the threshold of fluid-elastic instability has been numerically predicted via simulation of incompressible, unsteady, and turbulent cross-flow through a tube bundle in a normal triangular arrangement. the conditions of simulation i...

The conditions are investigated under which delay in ratio-dependent predatorprey systems cannot cause instability in higher dimension. We give an example when delay causes instability. Dedicated to the memory of Professor Miklós FARKAS 1 Model without delay ẋ = rxg(x,K)− n ∑

Recent developments in the design and manufacture of microcomputers together with improved simulation techniques make it possible to achieve the speed and accuracy required for the dynamic simulation of power systems in real time. This paper presents some experimental results and outlines new ideas on hardware architecture, mathematical algorithms and software development for this purpose. The ...

In this study the interaction between self-excited and paramet rically excited oscillations in two-degree-of-freedom systems with quadratic nonlinearities is investigated. The fundamental parametric resonance of the first mode and 3:1 internal resonance is considered, followed by 1:2 internal and parametric resonances of the second mode. The method of multiple time scales is applied to derive f...