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

Andrey Nesterov

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arXiv · 2510.12550

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

Andrey Nesterov

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Abstract

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.

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Andrey Nesterov. 2025-10-14. Asymptotics of the solution of the Cauchy problem for a singularly perturbed system of hyperbolic equations. Part 2. Initial conditions. https://arxiv.org/abs/2510.12550

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