This article is cited in 2 scientific papers (total in 2 papers)
Singularly perturbed elliptic Dirichlet problem with a multiple root of the degenerate equation
V. F. Butuzov, V. A. Beloshapko
Lomonosov Moscow State University, GSP-1, 1-2 Leninskiye Gory, 119991, Russia
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.
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”, Model. Anal. Inform. Sist., 23:5 (2016), 515–528
Citation in format AMSBIB
\by V.~F.~Butuzov, V.~A.~Beloshapko
\paper Singularly perturbed elliptic Dirichlet problem with a multiple root of the degenerate equation
\jour Model. Anal. Inform. Sist.
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A. A. Bykov, K. E. Ermakova, “Exact solutions of equations of a nonstationary front with equilibrium points of a fractional order”, Comput. Math. Math. Phys., 58:12 (2018), 1977–1988
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