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ЖУРНАЛЫ // Eurasian Mathematical Journal // Архив

Eurasian Math. J., 2013, том 4, номер 2, страницы 64–81 (Mi emj124)

The small parameter method for regular linear differential equations on unbounded domains

G. A. Karapetyan, H. G. Tananyan

Department of Applied Mathematics and Informatics, Russian-Armenian (Slavonic) University, Yerevan, Armenia

Аннотация: Algorithms for the asymptotic expansion of the solution to the Dirichlet problem for a regular equation with a small parameter $\varepsilon$ ($\varepsilon>0$) at higher derivatives on an unbounded domain (the whole space, the half space and a strip), based on the solution to the degenerate (as $\varepsilon\to0$) Dirichlet problem for a regular hypoelliptic equation of the lower order, are described. Estimates for remainder terms of those expansions are obtained.

Ключевые слова и фразы: regular operator, hypoelliptic operator, boundary layer, regular degeneration, singular perturbation, uniform solvability.

MSC: 35H10, 35B25, 41A80

Поступила в редакцию: 23.01.2012

Язык публикации: английский



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