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Model. Anal. Inform. Sist., 2017, Volume 24, Number 3, Pages 288–308 (Mi mais565)  

On contrast structures with a multizonal interior layer

V. F. Butuzov

Lomonosov Moscow State University, 1/2 Leninskie Gori, Moscow 119991

Abstract: A boundary value problem for a singularly perturbed differential equation of second order is considered in two cases, when one root of the degenerate equation is two-tuple. It is proved that in the first case the problem has a solution with the transition from the two-tuple root of the degenerate equation to one-tuple root in the small neighbourhood of an internal point of the interval, and in the second case the problem has a solution which has the spike in the interior layer. Such solutions are named, correspondingly, a contrast structure of step-type and a contrast structure of spike-type. In each case the asymptotic expansion of the contrast structure is constructed. It distinguishes from the known expansion in the case, when all the roots of the degenerate equation are one-tuple, in particular, the interior layer is multizonal.

Keywords: singularly perturbed equation, interior transitional layer, contrast structures of step type and spike type, asymptotic expansion of solution.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-04619_а
This work was supported by RFBR, project No 15-01-04619.


DOI: https://doi.org/10.18255/1818-1015-2017-3-288-308

Full text: PDF file (603 kB)
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UDC: 517.228.4
Received: 15.12.2016

Citation: V. F. Butuzov, “On contrast structures with a multizonal interior layer”, Model. Anal. Inform. Sist., 24:3 (2017), 288–308

Citation in format AMSBIB
\Bibitem{But17}
\by V.~F.~Butuzov
\paper On contrast structures with a multizonal interior layer
\jour Model. Anal. Inform. Sist.
\yr 2017
\vol 24
\issue 3
\pages 288--308
\mathnet{http://mi.mathnet.ru/mais565}
\crossref{https://doi.org/10.18255/1818-1015-2017-3-288-308}
\elib{http://elibrary.ru/item.asp?id=29332972}


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