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Asymptotics of the Solution to the Cauchy Problem for a Singularly Perturbed Operator Differential Transport Equation in Several Space Variables

Authors
  • Zaborskii, A. V.1
  • Nesterov, A. V.2
  • Nechaev, D. Yu.2
  • 1 “RADICO” Scientific Production Company, Obninsk, Kaluga oblast, 249035, Russia , Obninsk (Russia)
  • 2 Plekhanov Russian University of Economic, Moscow, 117997, Russia , Moscow (Russia)
Type
Published Article
Journal
Computational Mathematics and Mathematical Physics
Publisher
Pleiades Publishing
Publication Date
Dec 01, 2021
Volume
61
Issue
12
Pages
2015–2023
Identifiers
DOI: 10.1134/S0965542521120174
Source
Springer Nature
Keywords
Disciplines
  • Partial Differential Equations
License
Yellow

Abstract

AbstractA formal asymptotic expansion of the solution to the Cauchy problem for a singularly perturbed operator differential transport equation in several space variables with weak nonlinearity is constructed. Under certain conditions imposed on the data of the problem, the asymptotic expansion is constructed in the form of series in powers of a small parameter with coefficients depending on various stretched variables. Problems for determining all terms of the asymptotic expansion are obtained. Specifically, the leading term is determined as the solution of the Cauchy problem for a parabolic equation. The remainder is estimated with respect to the residual.

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