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This article is cited in 4 scientific papers (total in 4 papers)
Partial Differential Equations
Asymptotics of the solution to the Cauchy problem for a singularly perturbed operator differential transport equation in several space variables
A. V. Zaborskiya, A. V. Nesterovb, D. Yu. Nechaevb a "RADICO" Scientific Production Company, 249035, Obninsk, Kaluga oblast, Russia
b Plekhanov Russian University of Economic, 117997, Moscow, Russia
Abstract:
A 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.
Key words:
partial differential operator equations, Cauchy problem, small nonlinearity, singular perturbations, asymptotic expansions, parabolic equations.
Received: 16.02.2021 Revised: 28.04.2021 Accepted: 04.08.2021
Citation:
A. V. Zaborskiy, A. V. Nesterov, D. Yu. Nechaev, “Asymptotics of the solution to the Cauchy problem for a singularly perturbed operator differential transport equation in several space variables”, Zh. Vychisl. Mat. Mat. Fiz., 61:12 (2021), 2050–2058; Comput. Math. Math. Phys., 61:12 (2021), 2015–2023
Linking options:
https://www.mathnet.ru/eng/zvmmf11330 https://www.mathnet.ru/eng/zvmmf/v61/i12/p2050
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