scholarly journals Robustness of Polynomial Stability of Damped Wave Equations

2022 ◽  
Author(s):  
Dmytro Baidiuk ◽  
Lassi Paunonen
Keyword(s):  
Boundary Condition ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Polynomial Stability ◽  
One Dimensional ◽  
Acoustic Boundary Condition ◽  
The Stability ◽  
Perturbed Equation ◽  
Dimensional Wave

AbstractIn this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional wave equations on rectangular domains, a one-dimensional weakly damped Webster’s equation, and a wave equation with an acoustic boundary condition. In the case of Webster’s equation, we use our results to compute explicit numerical bounds that guarantee the polynomial stability of the perturbed equation.

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

On the metric perturbations of the Reissner–Nordström black hole

1979 ◽  
Vol 367 (1728) ◽  
pp. 1-14 ◽  
Keyword(s):  
Black Hole ◽  
Wave Equations ◽  
Schwarzschild Black Hole ◽  
One Dimensional ◽  
Dimensional Wave

The two pairs of one-dimensional wave equations which govern the odd and the even-parity perturbations of the Reissner–Nordström black hole are derived directly from a treatment of its metric perturbations. The treatment closely parallels the corresponding treatment in the context of the Schwarzschild black hole.

Chaos in the Rulkov Neuron Model Based on Marotto’s Theorem

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Penghe Ge ◽  
Hongjun Cao
Keyword(s):  
Neuron Model ◽  
Initial Conditions ◽  
Stability Conditions ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Fast Subsystem ◽  
One Dimensional ◽  
Sensitive Dependence ◽  
The Stability ◽  
Slow Subsystem

The existence of chaos in the Rulkov neuron model is proved based on Marotto’s theorem. Firstly, the stability conditions of the model are briefly renewed through analyzing the eigenvalues of the model, which are very important preconditions for the existence of a snap-back repeller. Secondly, the Rulkov neuron model is decomposed to a one-dimensional fast subsystem and a one-dimensional slow subsystem by the fast–slow dynamics technique, in which the fast subsystem has sensitive dependence on the initial conditions and its snap-back repeller and chaos can be verified by numerical methods, such as waveforms, Lyapunov exponents, and bifurcation diagrams. Thirdly, for the two-dimensional Rulkov neuron model, it is proved that there exists a snap-back repeller under two iterations by illustrating the existence of an intersection of three surfaces, which pave a new way to identify the existence of a snap-back repeller.

scholarly journals On the Stability of Evolution Galerkin Schemes Applied to a Two‐Dimensional Wave Equation System

2006 ◽  
Vol 44 (4) ◽  
pp. 1556-1583 ◽  
Author(s):  
M. Lukáčová‐Medviďová ◽  
G. Warnecke ◽  
Y. Zahaykah
Keyword(s):  
Wave Equation ◽  
Equation System ◽  
Two Dimensional ◽  
The Stability ◽  
Dimensional Wave
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