scholarly journals General stability and exponential growth of nonlinear variable coefficient wave equation with logarithmic source and memory term

2021 ◽  
Author(s):  
Long Yan ◽  
Lili Sun
Keyword(s):  
Wave Equation ◽  
Asymptotic Stability ◽  
Exponential Growth ◽  
Variable Coefficient ◽  
Nonlinear Damping ◽  
Memory Term ◽  
Weighted Energy Method ◽  
Weighted Energy ◽  
General Stability ◽  
Stability And Instability

This paper is concerned with the asymptotic stability and instability of solutions to a variable coefficient logarithmic wave equation with nonlinear damping and memory term. This model describes wave travelling through nonhomogeneous viscoelastic materials. By choosing appropriate multiplier and using weighted energy method, we prove the exponential decay of the energy. Besides, we also obtain the instability at the infinity of the solutions in the presence of the nonlinear damping.

scholarly journals L-asymptotic stability analysis of a 1D wave equation with a nonlinear damping

2020 ◽  
Vol 269 (10) ◽  
pp. 8107-8131
Author(s):  
Yacine Chitour ◽  
Swann Marx ◽  
Christophe Prieur
Keyword(s):  
Wave Equation ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Nonlinear Damping

scholarly journals On asymptotic behavior of solution to a nonlinear wave equation with Space-time speed of propagation and damping terms

2021 ◽  
Vol 40 (6) ◽  
pp. 1615-1639
Author(s):  
Paul A. Ogbiyele ◽  
Peter O. Arawomo
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Space Time ◽  
Decay Estimates ◽  
Damped Wave Equation ◽  
Asymptotic Behavior Of Solution ◽  
Weighted Energy Method ◽  
Weighted Energy ◽  
Speed Of Propagation ◽  
Nonlinear Damped Wave Equation

In this paper, we consider the asymptotic behavior of solution to the nonlinear damped wave equation utt – div(a(t, x)∇u) + b(t, x)ut = −|u|p−1u t ∈ [0, ∞), x ∈ Rn u(0, x) = u0(x), ut(0, x) = u1(x) x ∈ Rn with space-time speed of propagation and damping potential. We obtained L2 decay estimates via the weighted energy method and under certain suitable assumptions on the functions a(t, x) and b(t, x). The technique follows that of Lin et al.[8] with modification to the region of consideration in Rn. These decay result extends the results in the literature.

Asymptotic Behavior of Solution for Higher-Order Wave Equation

2013 ◽  
Vol 411-414 ◽  
pp. 1419-1422
Author(s):  
Wan Zhen Zhu ◽  
Yao Jun Ye
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Asymptotic Stability ◽  
Boundary Value Problem ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
Initial Boundary Value ◽  
Damping And Source Terms

In this paper the asymptotic stability of global solutions to the initial-boundary value problem for some nonlinear wave equation with nonlinear damping and source terms is studied by using a difference ineauality.

The time-asymptotic stability of shocks in cosmic-ray hydrodynamics

1988 ◽  
Vol 39 (3) ◽  
pp. 539-548 ◽  
Author(s):  
G. P. Zank
Keyword(s):  
Wave Equation ◽  
Asymptotic Stability ◽  
Short Wavelength ◽  
Cosmic Ray ◽  
Hydrodynamical Model ◽  
Shock Formation ◽  
Nonlinear Behaviour ◽  
Two Fluid

The nonlinear behaviour of short-wavelength perturbations in the two-fluid cosmic-ray hydrodynamical model is examined. We show that such a perturbation leads to shock formation and derive the appropriate wave equation. We show that a discontinuous perturbation incident on a weak cosmic-ray shock destabilizes, in a time-asymptotic sense, the shock.

scholarly journals Almost sure asymptotic stability analysis of the θ-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations

2012 ◽  
Vol 15 ◽  
pp. 71-83 ◽  
Author(s):  
Gregory Berkolaiko ◽  
Evelyn Buckwar ◽  
Cónall Kelly ◽  
Alexandra Rodkina
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Equilibrium Solution ◽  
Test System ◽  
Dimensional System ◽  
Step Size ◽  
Stochastic Perturbations ◽  
Stability And Instability

AbstractWe perform an almost sure linear stability analysis of the θ-Maruyama method, selecting as our test equation a two-dimensional system of Itô differential equations with diagonal drift coefficient and two independent stochastic perturbations which capture the stabilising and destabilising roles of feedback geometry in the almost sure asymptotic stability of the equilibrium solution. For small values of the constant step-size parameter, we derive close-to-sharp conditions for the almost sure asymptotic stability and instability of the equilibrium solution of the discretisation that match those of the original test system. Our investigation demonstrates the use of a discrete form of the Itô formula in the context of an almost sure linear stability analysis.

Sign in / Sign up

Export Citation Format

Share Document