Name: Partial Differential Equations V(Springer Verlag Gmbh) (en Inglés)
SKU: 62111500
Price: 95.37 USD
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Author: Fedoryuk M. V.,Joel J. S.,Babich V. M.

portada Partial Differential Equations V(Springer Verlag Gmbh) (en Inglés)

Partial Differential Equations V(Springer Verlag Gmbh) (en Inglés)

Formato

Libro Físico

Editorial

Springer Verlag Gmbh

Autor

Fedoryuk M. V.,Joel J. S.,Babich V. M.

Idioma

Inglés

N° páginas

247

Encuadernación

Tapa Blanda

ISBN13

9783642635861

Partial Differential Equations V(Springer Verlag Gmbh) (en Inglés)

Fedoryuk M. V.,Joel J. S.,Babich V. M. (Autor) · Springer Verlag Gmbh · Tapa Blanda

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Reseña del libro "Partial Differential Equations V(Springer Verlag Gmbh) (en Inglés)"

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.