Applied Mathematics and Mechanics

, Volume 7, Issue 3, pp 215–222 | Cite as

Interior layer phenomena of semilinear systems

  • Lin Zong-chi
  • Lin Su-rong
Article

Abstract

In this paper, we study the interior layer phenomena of singular perturbation boundary value problems for semilinear systems:
$$\begin{gathered} \varepsilon y = f\left( {t, y, \varepsilon } \right) \left( {a< t< b} \right) \hfill \\ y\left( {a, \varepsilon } \right) = A\left( \varepsilon \right), y\left( {b, \varepsilon } \right) = B\left( \varepsilon \right) \hfill \\ \end{gathered} $$
where ɛ>0 is a small parameter, y, f, A and B are n-dimensional vector functions. This vector boundary value peoblem does not appear to have been studied, although the scalar boundary problem has been treated extensively. Under appropriate assumptions we obtain existence of solution as in the scalar problem and the estimate of this solution in terms of appropriate inequalities as well.

Keywords

Mathematical Modeling Industrial Mathematic Small Parameter Vector Function Boundary Problem 

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References

  1. [1]
    Chang K.W. and F.A. Howes,Nonlinear Singular Perturbation Phenomena. Springer-Verlag Pub (in press)Google Scholar
  2. [2]
    Bernfeld, S. and V. Lakshmckautham, An Introduction to Non-linear Boundary Value Problems, Academic Press, New York (1974).Google Scholar
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    Hebets, P. and M. Laloy, E'tud de problèmes aux limites par la méthod des sur-et soussolutions, Lecture notes, Catholic University of Louvain (1974).Google Scholar
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    Chang, K.W. and G.X.Lin, Boundary and angular layer behavior in singularly perturbed semilinear systems.Appl. Math. and Mech. Vol. 5, No. 3 (1984).Google Scholar
  5. [5]
    Lin Zong-chi, The estimation of singular perturbation boundary value problem for a semilinear system, (in press)Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1986

Authors and Affiliations

  • Lin Zong-chi
    • 1
  • Lin Su-rong
    • 2
  1. 1.Fujian Normal UniversityFuzhou
  2. 2.Fujian Broadcasted TV UniversityFuzhou

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