Singularly perturbed elliptic Dirichlet problem with three-band boundary layer
V. A. Beloshapko
Lomonosov Moscow State University,
1 Leninskiye Gory, Moscow 119991, Russia
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.
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. A. Beloshapko, “Singularly perturbed elliptic Dirichlet problem with three-band boundary layer”, Model. Anal. Inform. Sist., 24:3 (2017), 280–287
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\paper Singularly perturbed elliptic Dirichlet problem with three-band boundary layer
\jour Model. Anal. Inform. Sist.
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