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. 
@article{MAIS_2016_23_5_a0,
     author = {V. F. Butuzov and V. A. Beloshapko},
     title = {Singularly perturbed elliptic {Dirichlet} problem with a multiple root of the degenerate equation},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {515--528},
     publisher = {mathdoc},
     volume = {23},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2016_23_5_a0/}
}
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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/