ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Example of Solution of a Singularly Perturbed Cauchy Problem for a Parabolic Eqiuation in the Presence of "strong" Turning Point


Alexander Georgievich Eliseev

Department of Higher Mathematics, Associate Professor
National Research University MPEI
14 Krasnokazarmennaya St., Moscow, Russia, 111250


In the article, on the basis of S.A. Lomov's regularization method, an asymptotic solution of a singularly perturbed Cauchy problem for a parabolic equation in the presence of a "strong" turning point is constructed. The regularization method makes it possible to construct an asymptotic solution uniform on the entire axis. The idea of this paper goes back to the paper where methods for solving a singularly perturbed Cauchy problem in the case of a "simple" turning point of a limit operator with a natural exponent were developed.



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