On contrast structures with a multizonal interior layer
V. F. Butuzov
Lomonosov Moscow State University, 1/2 Leninskie Gori, Moscow 119991
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.
singularly perturbed equation, interior transitional layer, contrast structures of step type and spike type, asymptotic expansion of solution.
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V. F. Butuzov, “On contrast structures with a multizonal interior layer”, Model. Anal. Inform. Sist., 24:3 (2017), 288–308
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\paper On contrast structures with a multizonal interior layer
\jour Model. Anal. Inform. Sist.
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