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Semilinear Singular Perturbation Problems

  • K. W. Chang
  • F. A. Howes
Part of the Applied Mathematical Sciences book series (AMS, volume 56)

Abstract

We consider first the semilinear Dirichlet problem

$$ \begin{gathered} \varepsilon y'' = h(t,y), a < t < b, \hfill \\ y(a,\varepsilon ) = A, y(b,\varepsilon ) = B, \hfill \\ \end{gathered} $$
(DP1)

where e is a small positive parameter and prime denotes differentiation with respect to t. Some natural questions to ask regarding this problem are: Does the problem have a solution for all small values of ε? Once the existence of a solution has been established, how does the solution behave as ε + 0+?

Keywords

Positive Constant Dirichlet Problem Stable Solution Shock Layer Fixed Constant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • K. W. Chang
    • 1
  • F. A. Howes
    • 2
  1. 1.Department of MathematicsUniversity of CalgaryCalgaryCanada
  2. 2.Department of MathematicsUniversity of CaliforniaDavisUSA

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