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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/3519

Title: TRANSITION TIME ANALYSIS IN SINGULARLY PERTURBED BOUNDARY-VALUE-PROBLEMS
Authors: DUMORTIER, Freddy
SMITS, Bert
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.
URI: http://hdl.handle.net/1942/3519
ISI #: A1995TB66400015
ISSN: 0002-9947
Type: Journal Contribution
Appears in Collections: Dynamical Systems

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