scholarly journals Some Results On The Asymptotic Behavior Of Linear Systems

1955 ◽  
Vol 7 ◽  
pp. 531-538 ◽  
Author(s):  
M. Marcus
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Matrix Differential Equation ◽  
Complex Matrix ◽  
Continuous Complex ◽  
Matrix Differential ◽  
Image Position ◽  
Vector Matrix ◽  
Complex Valued ◽  
Square Complex

1. Introduction. We consider first in §2 the asymptotic behavior as t → ∞ of the solutions of the vector-matrix differential equation(1.1) ,where A is a constant n-square complex matrix, B{t) a continuous complex valued n-square matrix defined on [0, ∞ ), and x a complex n-vector.

scholarly journals Existence of Ψ Bounded Solutions for a Lyapunov Matrix Dierential Equation

2014 ◽  
Vol 52 (2) ◽  
Author(s):  
Aurel Diamandescu
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Bounded Solution ◽  
Sufficient Condition ◽  
Matrix Differential Equation ◽  
Bounded Solutions ◽  
Necessary And Sufficient Condition ◽  
Lyapunov Matrix ◽  
Matrix Differential ◽  
Necessary And Sufficient

AbstractIt is proved a necessary and sufficient condition for the existence of at least one Ψ- bounded solution of a linear non- homogeneous Lyapunov matrix differential equation. In addition, it is given a result in connection with the asymptotic behavior of the Ψ- bounded solutions of this equation.

Oscillation Criteria for Matrix Differential Inequalities(1)

1973 ◽  
Vol 16 (1) ◽  
pp. 5-10 ◽  
Author(s):  
W. Allegretto ◽  
L. Erbe
Keyword(s):  
Differential Equation ◽  
Sufficient Conditions ◽  
Positive Semidefinite ◽  
Matrix Functions ◽  
Differential Inequalities ◽  
Matrix Differential Equation ◽  
Oscillation Criteria ◽  
Matrix Differential ◽  
Image Position

Several authors have recently considered the problem of obtaining sufficient conditions for the oscillation of the quasilinear matrix differential equation(1)and the associated inequality VTLV ≤ 0 (as a form). Here A, B, and V are m x m matrix functions, A(x) is symmetric, positive semidefinite and continuous in an interval [a, ∞) and B(x,V, V') is symmetric and continuous in a≤ x < ∞ for all V and V'.

A Converse Problem in Matrix Differential Equations

1973 ◽  
Vol 16 (3) ◽  
pp. 401-403
Author(s):  
Warren E. Shreveo
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Matrix Differential Equation ◽  
Converse Problem ◽  
Matrix Differential Equations ◽  
Matrix Differential ◽  
Image Position

Suppose X and F are nxn matrix solutions of the n X n matrix differential equation(1)such that(2)where J is some interval.

A Note on the Generalized Thermoelasticity Theory With Memory-Dependent Derivatives

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Soumen Shaw
Keyword(s):  
Differential Equation ◽  
Generalized Thermoelasticity ◽  
Matrix Differential Equation ◽  
Qualitative Properties ◽  
Conduction Model ◽  
Matrix Differential ◽  
Vector Matrix ◽  
Fundamental Equations ◽  
Short Time ◽  
With Memory

In this note, two aspects in the theory of heat conduction model with memory-dependent derivatives (MDDs) are studied. First, the discontinuity solutions of the memory-dependent generalized thermoelasticity model are analyzed. The fundamental equations of the problem are expressed in the form of a vector matrix differential equation. Applying modal decomposition technique, the vector matrix differential equation is solved by eigenvalue approach in Laplace transform domain. In order to obtain the solution in the physical domain, an approximate method by using asymptotic expansion is applied for short-time domain and analyzed the nature of the waves and discontinuity of the solutions. Second, a suitable Lyapunov function, which will be an important tool to study several qualitative properties, is proposed.

scholarly journals Note on the existence of a Ψ-bounded solution for a Lyapunov matrix differential equation

2012 ◽  
Vol 45 (3) ◽  
Author(s):  
Aurel Diamandescu
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Bounded Solution ◽  
Sufficient Condition ◽  
Matrix Differential Equation ◽  
Bounded Solutions ◽  
Necessary And Sufficient Condition ◽  
Lyapunov Matrix ◽  
Matrix Differential ◽  
Necessary And Sufficient

AbstractIn this paper, we give a necessary and sufficient condition for the existence of at least one Ψ-bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation. In addition, we give a result in connection with the asymptotic behavior of the Ψ-bounded solutions of this equation.

scholarly journals Thermal Disturbances in Twinned Orthotropic Thermoelastic Material

2018 ◽  
Vol 23 (4) ◽  
pp. 897-910 ◽  
Author(s):  
L. Rani ◽  
V. Singh
Keyword(s):  
Fourier Transforms ◽  
Crystallographic Axis ◽  
Physical Domain ◽  
Matrix Differential Equation ◽  
Special Cases ◽  
Eigen Value ◽  
Basic Equations ◽  
Matrix Differential ◽  
Thermally Conducting ◽  
Vector Matrix

Abstract This paper deals with deformation in homogeneous, thermally conducting, single-crystal orthotropic twins, bounded symmetrically along a plane containing only one common crystallographic axis. The Fourier transforms technique is applied to basic equations to form a vector matrix differential equation, which is then solved by the eigen value approach. The solution obtained is applied to specific problems of an orthotropic twin crystal subjected to triangular loading. The components of displacement, stresses and temperature distribution so obtained in the physical domain are computed numerically. A numerical inversion technique has been used to obtain the components in the physical domain. Particular cases as quasi-static thermo-elastic and static thermoelastic as well as special cases are also discussed in the context of the problem.

scholarly journals ON CONDITIONING FOR A GENERAL SYSTEM OF FOUR POINT BOUNDARY VALUE PROBLEMS

1996 ◽  
Vol 27 (3) ◽  
pp. 219-225
Author(s):  
M. S. N. MURTY
Keyword(s):  
Differential Equation ◽  
Fundamental Matrix ◽  
Close Relationships ◽  
General System ◽  
Point Boundary ◽  
Matrix Differential Equation ◽  
Growth Behaviour ◽  
First Order ◽  
Matrix Differential ◽  
The Stability

In this paper we investigate the close relationships between the stability constants and the growth behaviour of the fundamental matrix to the general FPBVP'S associated with the general first order matrix differential equation.

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