Geodesic
On contrast structures with a multizonal interior layer
Modelirovanie i analiz informacionnyh sistem, Tome 24 (2017) no. 3, pp. 288-308

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MAIS_2017_24_3_a3,
     author = {V. F. Butuzov},
     title = {On contrast structures with a multizonal interior layer},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {288--308},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2017_24_3_a3/}
}
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V. F. Butuzov. On contrast structures with a multizonal interior layer. Modelirovanie i analiz informacionnyh sistem, Tome 24 (2017) no. 3, pp. 288-308. http://geodesic.mathdoc.fr/item/MAIS_2017_24_3_a3/