Asymptotic stability of traveling waves for a dissipative nonlinear evolution system

2015 ◽  
Vol 35 (6) ◽  
pp. 1325-1338 ◽  
Author(s):  
Mina JIANG ◽  
Jianlin XIANG
Keyword(s):  
Asymptotic Stability ◽  
Traveling Waves ◽  
Nonlinear Evolution ◽  
Evolution System

scholarly journals EFFECT OF CHARGE MODULATION ON THE ELECTROCONVECTIVE FLOW OF A LOW CONDUCTING LIQUID

2021 ◽  
Author(s):  
Oleg Nekrasov ◽  
Boris Smorodin
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Traveling Waves ◽  
Nonlinear Evolution ◽  
Fluid Layer ◽  
Conducting Liquid ◽  
Phase Velocities ◽  
Charge Modulation ◽  
Stable Solutions ◽  
Amplitude And Frequency Modulation

Nonlinear evolution of the electroconvective flow patterns is analysed in a horizontal low conductive fluid layer under heating  from above and under modulated charge injection.  To examine the complex evolution of the system, numerical simulations  are carried out using a finite difference method. The influence of  amplitude and   frequency modulation on the  oscillatory electroconvection is studied.    Traveling waves with modulated amplitudes and phase velocities and synchronously modulated patterns are found as stable solutions.

On coupled nonlinear evolution system of fractional order with a proportional delay

2021 ◽  
Author(s):  
Israr Ahmad ◽  
Hussam Alrabaiah ◽  
Kamal Shah ◽  
Juan J. Nieto ◽  
Ibrahim Mahariq ◽  
...  
Keyword(s):  
Fractional Order ◽  
Nonlinear Evolution ◽  
Proportional Delay ◽  
Evolution System

scholarly journals Stability of Traveling Waves to a Burgers Equation with 2nd-Order Nonlinear Diffusion

2022 ◽  
Vol 4 (1) ◽  
pp. 77-85
Author(s):  
Mohammad Ghani
Keyword(s):  
Asymptotic Stability ◽  
Small Perturbation ◽  
Traveling Waves ◽  
Traveling Wave ◽  
Nonlinear Diffusion ◽  
Wave Amplitude ◽  
Energy Estimate ◽  
Burgers Equation ◽  
Original Equation ◽  
The Stability

We are interested in the study of asymptotic stability for Burgers equation with second-order nonlinear diffusion. We first transform the original equation by the ansatz transformation to establish the existence of traveling wave. We further employ the energy estimate under small perturbation and arbitrary wave amplitude. This energy estimate is then used to establish the stability.

Asymptotic stability for nonlinear PDEs with hysteresis

1994 ◽  
Vol 5 (1) ◽  
pp. 39-56 ◽  
Author(s):  
Nobuyuki Kenmochi ◽  
Augusto Visintin
Keyword(s):  
Periodic Solution ◽  
Asymptotic Stability ◽  
Evolution Equations ◽  
Stable Equilibrium ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Nonlinear Pdes ◽  
Independent Function ◽  
Forcing Term ◽  
Stability Of The Solution

Nonlinear evolution equations including hysteresis functionals are studied. It is the purpose of this paper to investigate the asymptotic stability of the solution as time t → + ∞. In the case when the forcing term of the equation tends to a time-independent function as t → + ∞, we shall show that the solution stabilizes at + ∞ and the system is asymptotically stable (equilibrium stability). In the case when the forcing term is periodic in time, we shall show that there is at least one periodic solution and that in some restricted cases the periodic solution is unique.

Spectral broadening and flow randomization in free shear layers

2012 ◽  
Vol 706 ◽  
pp. 431-469 ◽  
Author(s):  
Xuesong Wu ◽  
Feng Tian
Keyword(s):  
Phase Modulation ◽  
Numerical Solutions ◽  
Nonlinear Evolution ◽  
Present Theory ◽  
Shear Layers ◽  
Evolution System ◽  
Free Shear Layer ◽  
Spectral Broadening ◽  
Free Shear Layers ◽  
Combination Frequencies

AbstractIt has been observed experimentally that when a free shear layer is perturbed by a disturbance consisting of two waves with frequencies ${\omega }_{0} $ and ${\omega }_{1} $, components with the combination frequencies $(m{\omega }_{0} \pm n{\omega }_{1} )$ ($m$ and $n$ being integers) develop to a significant level thereby causing flow randomization. This spectral broadening process is investigated theoretically for the case where the frequency difference $({\omega }_{0} \ensuremath{-} {\omega }_{1} )$ is small, so that the perturbation can be treated as a modulated wavetrain. A nonlinear evolution system governing the spectral dynamics is derived by using the non-equilibrium nonlinear critical layer approach. The formulation provides an appropriate mathematical description of the physical concepts of sideband instability and amplitude–phase modulation, which were suggested by experimentalists. Numerical solutions of the nonlinear evolution system indicate that the present theory captures measurements and observations rather well.

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