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Boundary and Angular Layer Behavior in Singularly Perturbed Semilinear Systems

Published online by Cambridge University Press:  20 November 2018

K. W. Chang  and
G. X. Liu
K. W. Chang
Affiliation:
Department of mathematics and statistics, The university of calgaryCalgary, alberta
G. X. Liu
Affiliation:
Department of mathematics, Nankai universityTiajin, china
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Abstract

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Some authors have employed the method and technique of differential inequalities to obtain fairly general results concerning the existence and asymptotic behavior, as ∊ → 0+, of the solutions of scalar boundary value problems

∊y" = h(t,y), a < t < b,

y(a,∊) = A, y(b,∊) = B.

In this paper, we extend these results to vector boundary value problems, under analogous stability conditions on the solution u = u(t) of the reduced equation 0 = h(t,u).

Two types of asymptotic behavior are studied, depending on whether the reduced solution u(t) has or does not have a continuous first derivative in (a,b), leading to the phenomena of boundary and angular layers.

Keywords

34D15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 2 , 01 June 1985 , pp. 174 - 183
Copyright
Copyright © Canadian Mathematical Society 1985

References

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