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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
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Homogenization of Multiple Integrals (Hardcover)
Loot Price: R4,390
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Homogenization of Multiple Integrals (Hardcover)
Series: Oxford Lecture Series in Mathematics and Its Applications, 12
Expected to ship within 12 - 17 working days
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The object of homogenization theory is the description of the
macroscopic properties of structures with fine microstructure,
covering a wide range of applications that run from the study of
properties of composites to optimal design. The structures under
consideration may model cellular elastic materials, fibred
materials, stratified or porous media, or materials with many holes
or cracks. In mathematical terms, this study can be translated in
the asymptotic analysis of fast-oscillating differential equations
or integral functionals. The book presents an introduction to the
mathematical theory of homogenization of nonlinear integral
functionals, with particular regard to those general results that
do not rely on smoothness or convexity assumptions. Homogenization
results and appropriate descriptive formulas are given for periodic
and almost- periodic functionals. The applications include the
asymptotic behaviour of oscillating energies describing cellular
hyperelastic materials, porous media, materials with stiff and soft
inclusions, fibered media, homogenization of HamiltonJacobi
equations and Riemannian metrics, materials with multiple scales of
microstructure and with multi-dimensional structure. The book
includes a specifically designed, self-contained and up-to-date
introduction to the relevant results of the direct methods of
Gamma-convergence and of the theory of weak lower semicontinuous
integral functionals depending on vector-valued functions. The book
is based on various courses taught at the advanced graduate level.
Prerequisites are a basic knowledge of Sobolev spaces, standard
functional analysis and measure theory. The presentation is
completed by several examples and exercises.
General
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