Singularly Perturbed Integro-Differential Systems with Kernels Depending on Solutions of Differential Equations
Bobodzhanov A.A. Kalimbetov B.T. Safonov V.F.
May 2023Pleiades Publishing
Differential Equations
2023#59Issue 5707 - 719 pp.
Abstract: We consider integro-differential equations (IDEs) with a rapidly oscillating inhomogeneityand with a Volterra-type integral operator whose kernels can contain both a classical rapidlydecreasing exponential (the simplest case) and fundamental solutions of differential systems (thegeneral case). Difficulty in constructing a regularized (according to S.A. Lomov) asymptotics inthe general case is due to the complex asymptotic structure of the fundamental solution matrix(Cauchy matrix) of the homogeneous differential system. In the present paper, we first construct aregularized asymptotics of the Cauchy matrix, which is then used to construct a regularizedasymptotics of the solution of the IDE.
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National Research University “Moscow Power Engineering Institute”, Moscow, 111250, Russian Federation
Mukhtar Auezov South Kazakhstan University, Shymkent, 160012, Kazakhstan
National Research University “Moscow Power Engineering Institute”
Mukhtar Auezov South Kazakhstan University
10 лет помогаем публиковать статьи Международный издатель
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