THE INTERIOR LAYER FOR A NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATION

doi:10.1016/S0252-9602(12)60049-6

Abstract

Abstract:

In this article, the interior layer for a second order nonlinear singularly per-turbed differential-difference equation is considered. Using the methods of boundary func-tion and fractional steps, we construct the formula of asymptotic expansion and point out that the boundary layer at t = 0 has a great influence upon the interior layer at t = σ. At the same time, on the basis of differential inequality techniques, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of our result. The result of this article is new and it complements the previously known ones.

Key words: Differential-difference equation, interior layer, asymptotic expansion, bound-ary function

CLC Number:

34E20

WANG Ai-Feng, NI Ming-Kang. THE INTERIOR LAYER FOR A NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATION[J].Acta mathematica scientia,Series B, 2012, 32(2): 695-709.

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