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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes (Hardcover, 2005 ed.)
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Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes (Hardcover, 2005 ed.)
Series: Springer Monographs in Mathematics
Expected to ship within 18 - 22 working days
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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."
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