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Andrey Nesterov

Publications and source records attributed to Andrey Nesterov.

3 recordsLinked to original sources
arXiv2025

Asymptotics of the solution of the Cauchy problem for a singularly perturbed system of hyperbolic equations. Part 2. Initial conditions

An asymptotic small parameter expansion of a single Cauchy problem is constructed for a singularly perturbed system of hyperbolic equations describing vibrations of two rigidly connected strings. Equations (such as generalized Korteweg-de Vriesequations) and initial conditions for the terms of the asymptotic expansion of the solution are determined, and under certain assumptions, the residual term is estimated from the residual.

math.AP↗
arXiv2023

Asymptotics of solving a singularly perturbed system of transport equations with fast and slow components in the critical case

An asymptotic expansion with respect to a small parameter of the solution of the Cauchy problem is constructed for a system of three transfer equations, two of which are singularly perturbed by the degeneracy of the entire senior part of the transfer operator, and the third equation clearly does not contain a small parameter. The peculiarity of the problem is that it belongs to the so-called critical case: the solution of a degenerate problem is a one-parameter family. The asymptotic expansion of the solution under smooth initial conditions is constructed as the sum of the regular part and boundary functions.

math.AP↗