Semilinear Singular Perturbation Problems

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


We consider first the semilinear Dirichlet problem

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

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+?


Positive Constant Dirichlet Problem Stable Solution Shock Layer Fixed Constant 
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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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