Geodesic
Singularly perturbed elliptic Dirichlet problem with a multiple root of the degenerate equation
Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 5, pp. 515-528.

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A singularly perturbed elliptic problem with Dirichlet boundary conditions is considered in the case of multiple roots of the degenerate equation. A complete asymptotic expansion of the solution is constructed and justified. It is qualitatively different from the known expansion in the case where the root of the degenerate equation is simple: the asymptotic expansion of the solution being in fractional powers of the small parameter, boundary-layer variables have a different scale, boundary-layer series is constructed using a non-standard algorithm, the boundary layer in the vicinity of the domain boundary consists of three zones with different behavior of the solution in different zones.
Keywords: singularly perturbed elliptic equation, case of multiple root of the degenerate equation, asymptotic expansion of boundary layer type solution, three-band boundary layer. 
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V. F. Butuzov; V. A. Beloshapko. Singularly perturbed elliptic Dirichlet problem with a multiple root of the degenerate equation. Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 5, pp. 515-528. http://geodesic.mathdoc.fr/item/MAIS_2016_23_5_a0/

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