Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes (Hardcover, 2005 ed.)

Variational and boundary integral equation techniques are two of the most useful methods for solving time-dependent problems described by systems of equations of the form 2 ? u = Au, 2 't 2 where u = u(x, t) is a vector-valued function, x is a point in a domain inR or 3 R, and A is a linear elliptic di?erential operator. To facilitate a better und- standing of these two types of methods, below we propose to illustrate their mechanisms in action on a speci?c mathematical model rather than in a more impersonal abstract setting. For this purpose, we have chosen the hyperbolic system of partial di?erential equations governing the nonstationary bending of elastic plates with transverse shear deformation. The reason for our choice is twofold. On the one hand, in a certain sense this is a hybrid system, c- sistingofthreeequationsforthreeunknownfunctionsinonlytwoindependent variables, which makes it more unusual and thereby more interesting to the analyst than other systems arising in solid mechanics. On the other hand, this particular plate model has received very little attention compared to the so-called classical one, based on Kirchho? s simplifying hypotheses, although, as acknowledged by practitioners, it represents a substantial re?nement of the latter and therefore needs a rigorous discussion of the existence, uniqueness, and continuous dependence of its solution on the data before any construction of numerical approximation algorithms can be contemplated."

General

Imprint:	Springer London
Country of origin:	United Kingdom
Series:	Springer Monographs in Mathematics
Release date:	February 2005
First published:	2005
Authors:	Igor Chudinovich
Dimensions:	235 x 155 x 11mm (L x W x T)
Format:	Hardcover
Pages:	148
Edition:	2005 ed.
ISBN-13:	978-1-85233-888-6
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
LSN:	1-85233-888-1
Barcode:	9781852338886

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