Surveys in Applied Mathematics: 001 (Surveys in Applied Mathematics, Vol 1)@7914 Rs [Mrp:-7914]

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Partial differential equations play a central role in many branches of science and engineering. Therefore it is important to solve problems involving them. One aspect of solving a partial differential equation problem is to show that it is well-posed, i. e. , that it has one and only one solution, and that the solution depends continuously on the data of the problem. Another aspect is to obtain detailed quantitative information about the solution. The traditional method for doing this was to find a representation of the solution as a series or integral of known special functions, and then to evaluate the series or integral by numerical or by asymptotic methods. The shortcoming of this method is that there are relatively few problems for which such representations can be found. Consequently, the traditional method has been replaced by methods for direct solution of problems either numerically or asymptotically. This article is devoted to a particular method, called the “ray method,” for the asymptotic solution of problems for linear partial differential equations governing wave propagation. These equations involve a parameter, such as the wavelength. . \, which is small compared to all other lengths in the problem. The ray method is used to construct an asymptotic expansion of the solution which is valid near . . \ = 0, or equivalently for k = 21r I A near infinity.

Product Details :

Author Joseph B. Keller
Author David W. McLaughlin
Author George C. Papanicolaou
Binding Hardcover
Brand imusti
EAN 9780306449932
Edition 1995
Format Import
ISBN 0306449935
Label Springer
Manufacturer Springer
NumberOfItems 1
NumberOfPages 264
PackageQuantity 1
ProductGroup Book
ProductTypeName ABIS_BOOK
PublicationDate 1995-08-31
Publisher Springer
Studio Springer
Title Surveys in Applied Mathematics: 001 (Surveys in Applied Mathematics, Vol 1)