scholarly journals A Discrete Analog of the Lyapunov Function for Hyperbolic Systems

2018 ◽  
Vol 64 (4) ◽  
pp. 591-602
Author(s):  
R D Aloev ◽  
M U Khudayberganov
Keyword(s):  
Lyapunov Function ◽  
Hyperbolic Systems ◽  
A Priori ◽  
A Priori Estimate ◽  
Discrete Analog ◽  
Priori Estimate ◽  
Constant Coefficients ◽  
The Difference ◽  
Dissipative Boundary ◽  
Linear Hyperbolic System

We study the difference splitting scheme for the numerical calculation of stable solutions of a two-dimensional linear hyperbolic system with dissipative boundary conditions in the case of constant coefficients with lower terms. A discrete analog of the Lyapunov function is constructed and an a priori estimate is obtained for it. The obtained a priori estimate allows us to assert the exponential stability of the numerical solution.

A Second-Order Three-Level Difference Scheme for a Magneto-Thermo-Elasticity Model

2014 ◽  
Vol 6 (3) ◽  
pp. 281-298 ◽  
Author(s):  
Hai-Yan Cao ◽  
Zhi-Zhong Sun ◽  
Xuan Zhao
Keyword(s):  
Difference Scheme ◽  
Hyperbolic Equations ◽  
A Priori ◽  
A Priori Estimate ◽  
Second Order ◽  
Priori Estimate ◽  
Third Order ◽  
The Third ◽  
The Difference ◽  
Second Order Convergence

AbstractThis article deals with the numerical solution to the magneto-thermo-elasticity model, which is a system of the third order partial differential equations. By introducing a new function, the model is transformed into a system of the second order generalized hyperbolic equations. A priori estimate with the conservation for the problem is established. Then a three-level finite difference scheme is derived. The unique solvability, unconditional stability and second-order convergence inL∞-norm of the difference scheme are proved. One numerical example is presented to demonstrate the accuracy and efficiency of the proposed method.

scholarly journals A PRIORI ESTIMATE FOR AN EQUATION WITH FRACTIONAL DERIVATIVES WITH DIFFERENT ORIGINS

2019 ◽  
pp. 41-47
Author(s):  
Л.М. Энеева
Keyword(s):  
Fractional Derivatives ◽  
Model Equation ◽  
A Priori ◽  
A Priori Estimate ◽  
Equation Of Motion ◽  
Point Boundary ◽  
Priori Estimate ◽  
Fractal Media ◽  
Different Origins ◽  
Variable Potential

В работе исследуется обыкновенное дифференциальное уравнение дробного порядка, содержащее композицию дробных производных с различными началами, с переменным потенциалом. Рассматриваемое уравнение выступает модельным уравнением движения во фрактальной среде. Для исследуемого уравнения доказана априорная оценка решения смешанной двухточечной краевой задачи. We consider an ordinary differential equation of fractional order with the composition of leftand right-sided fractional derivatives, and with variable potential. The considered equation is a model equation of motion in fractal media. We prove an a priori estimate for solutions of a mixed two-point boundary value problem for the equation under study.

scholarly journals On a class of singular hyperbolic equation with a weighted integral condition

1999 ◽  
Vol 22 (3) ◽  
pp. 511-519 ◽  
Author(s):  
Said Mesloub ◽  
Abdelfatah Bouziani
Keyword(s):  
Hyperbolic Equation ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Nonlocal Condition ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Priori Estimate ◽  
Weighted Integral

In this paper, we study a mixed problem with a nonlocal condition for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.

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