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|Title: ||TRANSITION TIME ANALYSIS IN SINGULARLY PERTURBED BOUNDARY-VALUE-PROBLEMS|
|Authors: ||DUMORTIER, Freddy|
|Issue Date: ||1995|
|Publisher: ||AMER MATHEMATICAL SOC|
|Citation: ||TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 347(10). p. 4129-4145|
|Abstract: ||The payer deals with the boundary value problem epsilon x + xx-x(2) = 0, with x(0) = A, x(T) = B for A, B, T > 0 and epsilon > 0 close to zero. It is shown that for T sufficiently big, the problem has exactly three solutions, two of which reach negative values. Solutions reaching negative values occur for T greater than or equal to T(epsilon) > 0 and we show that asymptotically for epsilon --> 0, T(epsilon) similar to ln (epsilon), i.e. lim(epsilon-->0) -T(epsilon)/ln(epsilon) = 1. The main tools are transit time analysis in the Lienard plane and normal form techniques. As such the methods are rather qualitative and useful in other similar problems.|
|Notes: ||DUMORTIER, F, LIMBURGS UNIV CENTRUM,DEPT WNI,UNIV CAMPUS,B-3590 DIEPENBEEK,BELGIUM.|
|ISI #: ||A1995TB66400015|
|Type: ||Journal Contribution|
|Appears in Collections: ||Dynamical Systems|
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