| 书目名称 | Partial Differential Equations V |
| 副标题 | Asymptotic Methods f |
| 编辑 | M. V. Fedoryuk |
| 视频video | |
| 概述 | The authors survey an important topic in PDE which is highly relevant for applications in physics |
| 丛书名称 | Encyclopaedia of Mathematical Sciences |
| 图书封面 |  |
| 描述 | In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the m |
| 出版日期 | Book 1999 |
| 关键词 | Asymptotic expansions; Boundary value problem; Differentialgleichngen; Mechanik der inhomogenen Medien; |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-642-58423-7 |
| isbn_softcover | 978-3-642-63586-1 |
| isbn_ebook | 978-3-642-58423-7Series ISSN 0938-0396 |
| issn_series | 0938-0396 |
| copyright | Springer-Verlag Berlin Heidelberg 1999 |
发表于 2025-3-21 17:04:07
