On the Comparison of Solutions of Related Properly and Improperly Posed Cauchy Problems for First Order Operator Equations

1982 ◽  
Vol 13 (4) ◽  
pp. 594-606 ◽  
Author(s):  
Karen A. Ames
Keyword(s):  
Cauchy Problems ◽  
Order Operator ◽  
Operator Equations ◽  
First Order

scholarly journals Formulae of partial reduction for linear systems of first order operator equations

2010 ◽  
Vol 23 (11) ◽  
pp. 1367-1371 ◽  
Author(s):  
Branko Malešević ◽  
Dragana Todorić ◽  
Ivana Jovović ◽  
Sonja Telebaković
Keyword(s):  
Linear Systems ◽  
Partial Reduction ◽  
Order Operator ◽  
Operator Equations ◽  
First Order

scholarly journals Differential Transcendency in the Theory of Linear Differential Systems with Constant Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Branko Malešević ◽  
Dragana Todorić ◽  
Ivana Jovović ◽  
Sonja Telebaković
Keyword(s):  
Cauchy Problem ◽  
Linear System ◽  
Order Operator ◽  
Operator Equations ◽  
Differential Systems ◽  
First Order ◽  
Linear Differential Systems ◽  
Constant Coefficients ◽  
Linear Differential

We consider a reduction of a nonhomogeneous linear system of first-order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant coefficients and to the question of differential transcendency.

On the Strong Stability of First-Order Operator-Differential Equations

2004 ◽  
Vol 40 (5) ◽  
pp. 703-710 ◽  
Author(s):  
D. R. Bojovic ◽  
B. S. Jovanovic ◽  
P. P. Matus
Keyword(s):  
Differential Equations ◽  
Strong Stability ◽  
Order Operator ◽  
First Order

7.—Elliptic Singular Perturbations of First-order Operators with Critical Points

1976 ◽  
Vol 74 ◽  
pp. 91-113 ◽  
Author(s):  
P. P. N. de Groen
Keyword(s):  
Boundary Value Problem ◽  
Critical Points ◽  
Elliptic Boundary ◽  
Elliptic Boundary Value Problem ◽  
Internal Layers ◽  
Order Operator ◽  
Elliptic Boundary Value ◽  
First Order ◽  
Special Values ◽  
Image Position

SynopsisWe study the asymptotic behaviour for ɛ→+0 of the solution Φ of the elliptic boundary value problemis a bounded domain in ℝ2, 2 is asecond-order uniformly elliptic operator, 1 is a first-order operator, which has critical points in the interior of , i.e. points at which the coefficients of the first derivatives vanish, ɛ and μ are real parameters and h is a smooth function on . We construct firstorder approximations to Φ for all types of nondegenerate critical points of 1 and prove their validity under some restriction on the range of μ.In a number of cases we get internal layers of nonuniformity (which extend to the boundary in the saddle-point case) near the critical points; this depends on the position of the characteristics of 1 and their direction. At special values of the parameter μ outside the range in which we could prove validity we observe ‘resonance’, a sudden displacement of boundary layers; these points are connected with the spectrum of the operator ɛ2 + 1 subject to boundary conditions of Dirichlet type.

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