Singularly Perturbed System of Parabolic Equations in the Critical Case

2018 ◽  
Vol 230 (5) ◽  
pp. 728-731 ◽  
Author(s):  
A. S. Omuraliev ◽  
S. Kulmanbetova
Keyword(s):  
Parabolic Equations ◽  
Critical Case ◽  
Singularly Perturbed ◽  
Singularly Perturbed System ◽  
Perturbed System ◽  
System Of Parabolic Equations

scholarly journals Constructive method for solving a nonlinear singularly perturbed system of differential equations in critical case

1993 ◽  
Vol 6 (1) ◽  
pp. 69-81
Author(s):  
Angela Slavova
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Critical Case ◽  
Singularly Perturbed ◽  
Constructive Method ◽  
System Of Differential Equations ◽  
Singularly Perturbed System ◽  
Perturbed System ◽  
Degenerate Matrix

A singularly, perturbed system of differential equations with degenerate matrix at the derivative is considered. The existence and construction of the periodic solutions are investigated in critical case. For the analysis of these algorithms the apparatus of Lyapunov's finite majorizing equations is used. An implementation of this method is given in two examples.

scholarly journals Complete Controllability Conditions for Linear Singularly Perturbed Time-Invariant Systems with Multiple Delays via Chang-Type Transformation

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 71 ◽  
Author(s):  
Olga Tsekhan
Keyword(s):  
Sufficient Conditions ◽  
Singularly Perturbed ◽  
Degenerate System ◽  
Multiple Delays ◽  
Complete Controllability ◽  
Singularly Perturbed System ◽  
System With Delay ◽  
Perturbed System ◽  
Time Invariant ◽  
Controllability Conditions

The problem of complete controllability of a linear time-invariant singularly-perturbed system with multiple commensurate non-small delays in the slow state variables is considered. An approach to the time-scale separation of the original singularly-perturbed system by means of Chang-type non-degenerate transformation, generalized for the system with delay, is used. Sufficient conditions for complete controllability of the singularly-perturbed system with delay are obtained. The conditions do not depend on a singularity parameter and are valid for all its sufficiently small values. The conditions have a parametric rank form and are expressed in terms of the controllability conditions of two systems of a lower dimension than the original one: the degenerate system and the boundary layer system.

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