Asymptotic Analysis For Periodic Structures (studies In Mathematics And Its Applications)
1978 / English / DjVu
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This is a reprinting of a book originally published in 1978. At
that time it was the first book on the subject of homogenization,
which is the asymptotic analysis of partial differential equations
with rapidly oscillating coefficients, and as such it sets the
stage for what problems to consider and what methods to use,
including probabilistic methods. At the time the book was written
the use of asymptotic expansions with multiple scales was new,
especially their use as a theoretical tool, combined with energy
methods and the construction of test functions for analysis with
weak convergence methods. Before this book, multiple scale methods
were primarily used for non-linear oscillation problems in the
applied mathematics community, not for analyzing spatial
oscillations as in homogenization. In the current printing a number
of minor corrections have been made, and the bibliography was
significantly expanded to include some of the most important recent
references. This book gives systematic introduction of multiple
scale methods for partial differential equations, including their
original use for rigorous mathematical analysis in elliptic,
parabolic, and hyperbolic problems, and with the use of
probabilistic methods when appropriate. The book continues to be
interesting and useful to readers of different backgrounds, both
from pure and applied mathematics, because of its informal style of
introducing the multiple scale methodology and the detailed proofs.
This is a reprinting of a book originally published in 1978. At
that time it was the first book on the subject of homogenization,
which is the asymptotic analysis of partial differential equations
with rapidly oscillating coefficients, and as such it sets the
stage for what problems to consider and what methods to use,
including probabilistic methods. At the time the book was written
the use of asymptotic expansions with multiple scales was new,
especially their use as a theoretical tool, combined with energy
methods and the construction of test functions for analysis with
weak convergence methods. Before this book, multiple scale methods
were primarily used for non-linear oscillation problems in the
applied mathematics community, not for analyzing spatial
oscillations as in homogenization. In the current printing a number
of minor corrections have been made, and the bibliography was
significantly expanded to include some of the most important recent
references. This book gives systematic introduction of multiple
scale methods for partial differential equations, including their
original use for rigorous mathematical analysis in elliptic,
parabolic, and hyperbolic problems, and with the use of
probabilistic methods when appropriate. The book continues to be
interesting and useful to readers of different backgrounds, both
from pure and applied mathematics, because of its informal style of
introducing the multiple scale methodology and the detailed proofs.
