Partial Differential Equations V | Asymptotic Methods for Partial Differential Equations

M. V. Fedoryuk

ISBN 10: 3642635865 / ISBN 13: 9783642635861

Published by Springer, 2012

About this Item

Partial Differential Equations V | Asymptotic Methods for Partial Differential Equations | M. V. Fedoryuk | Taschenbuch | Encyclopaedia of Mathematical Sciences | vii | Englisch | 2012 | Springer | EAN 9783642635861 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.

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Bibliographic Details

• Title: Partial Differential Equations V | Asymptotic Methods for Partial Differential Equations
• Publisher: Springer
• Publication Date: 2012
• Language: English
• ISBN 10: 3642635865
• ISBN 13: 9783642635861
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 15D millimeters 235 millimeters width by 155 millimeters height by 15 millimeters depth
• Weight: 400 grams
• Seller catalogs:
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About this title

Synopsis

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 method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.