Geodesic
Singularly perturbed elliptic Dirichlet problem with three-band boundary layer
Modelirovanie i analiz informacionnyh sistem, Tome 24 (2017) no. 3, pp. 280-287

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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 three-zone boundary layer arises in the vicinity of the domain boundary with a different scale of boundary-layer variables and a different behaviour of the solution in different zones. The asymptotic expansion of the solution being in fractional powers of the small parameter, boundary-layer series are constructed using a non-standard algorithm. A complete asymptotic expansion of the solution is constructed and justified.
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_2017_24_3_a2,
     author = {V. A. Beloshapko},
     title = {Singularly perturbed elliptic {Dirichlet} problem with three-band boundary layer},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {280--287},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2017_24_3_a2/}
}
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V. A. Beloshapko. Singularly perturbed elliptic Dirichlet problem with three-band boundary layer. Modelirovanie i analiz informacionnyh sistem, Tome 24 (2017) no. 3, pp. 280-287. http://geodesic.mathdoc.fr/item/MAIS_2017_24_3_a2/