Automatically identifying the asymptotic behavior of nonlinear singularly perturbed boundary value problems

1992 ◽  
Vol 8 (3) ◽  
pp. 395-419 ◽  
Author(s):  
Mark F. Russo ◽  
Richard L. Peskin
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Singularly Perturbed

Boundary and Angular Layer Behavior in Singularly Perturbed Semilinear Systems

1985 ◽  
Vol 28 (2) ◽  
pp. 174-183
Author(s):  
K. W. Chang ◽  
G. X. Liu
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Stability Conditions ◽  
Differential Inequalities ◽  
Semilinear Systems ◽  
First Derivative ◽  
Layer Behavior

AbstractSome 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.

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