Asymptotics of the solution of the Cauchy problem for a singularly perturbed system of hyperbolic equations. Part 2. Initial conditions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912646893142016 |
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| author | Nesterov, Andrey |
| author_facet | Nesterov, Andrey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12550 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics of the solution of the Cauchy problem for a singularly perturbed system of hyperbolic equations. Part 2. Initial conditions Nesterov, Andrey Analysis of PDEs 35C20 (Primary) 35E15, 35L15 (Secondary) 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. |
| title | Asymptotics of the solution of the Cauchy problem for a singularly perturbed system of hyperbolic equations. Part 2. Initial conditions |
| topic | Analysis of PDEs 35C20 (Primary) 35E15, 35L15 (Secondary) |
| url | https://arxiv.org/abs/2510.12550 |