scholarly journals Asymptotic stability of an integro-differential equation of parabolic type

1986 ◽  
Vol 47 (1) ◽  
pp. 65-78
Author(s):  
Danuta Jama
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Parabolic Type ◽  
Integro Differential Equation

scholarly journals Lyapunov-Krasovskii stability analysis of nonlinear integro-differential equation

2018 ◽  
Vol 7 (2) ◽  
pp. 53
Author(s):  
Prebo Jackreece
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Asymptotic Stability ◽  
Integro Differential Equation ◽  
Necessary And Sufficient

The purpose of this paper is to develop a qualitative stability analysis of a class of nonlinear integro-differential equation within the framework of Lyapunov-Krasovskii. We show that the existence of a Lyapunov-Krasovskii functional is a necessary and sufficient condition for the uniform asymptotic stability of the nonlinear Volterra integro-differential equations.

Averaged semi-discrete scheme of sum-approximation for one nonlinear multi-dimensional integro-differential parabolic equation

2020 ◽  
Vol 27 (3) ◽  
pp. 367-373
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Differential Equation ◽  
Electromagnetic Field ◽  
Parabolic Equation ◽  
Mathematical Simulation ◽  
Parabolic Type ◽  
Integro Differential Equation ◽  
Discrete Scheme ◽  
Maxwell’S System ◽  
Field Penetration

AbstractThe paper is devoted to the construction and study of the additive averaged semi-discrete scheme for one nonlinear multi-dimensional integro-differential equation of parabolic type. The studied equation is based on the well-known Maxwell’s system arising in mathematical simulation of electromagnetic field penetration into a substance.

scholarly journals ON SPECIFIC ASYMPTOTIC STABILITY SOLUTIONS OF A LINEAR HOMOGENEOUS WELTERER INTEGRO-DIFFERENTIAL EQUATION OF THE FOURTH ORDER

2021 ◽  
pp. 110-117
Author(s):  
Z. A. Japarova
Keyword(s):  
Differential Equation ◽  
Asymptotic Stability ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Third Order ◽  
Volterra Type ◽  
Integro Differential Equation ◽  
The Third ◽  
Fourth Order Differential Equation

Specific sufficient conditions for the asymptotic stability of a linear homogeneous fourthorder integro-differential equation of the Volterra type are established in the case when all nonzero solutions of the corresponding fourth-order differential equation do not have the property of asymptotic stability of the solutions. In this paper, we obtain estimates on the semiaxis of the solution and the derivative up to the third order.

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