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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Singular Perturbations and Boundary Layers (Hardcover, 1st ed. 2018)
Loot Price: R3,994
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Singular Perturbations and Boundary Layers (Hardcover, 1st ed. 2018)
Series: Applied Mathematical Sciences, 200
Expected to ship within 12 - 19 working days
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Singular perturbations occur when a small coefficient affects the
highest order derivatives in a system of partial differential
equations. From the physical point of view singular perturbations
generate in the system under consideration thin layers located
often but not always at the boundary of the domains that are called
boundary layers or internal layers if the layer is located inside
the domain. Important physical phenomena occur in boundary layers.
The most common boundary layers appear in fluid mechanics, e.g.,
the flow of air around an airfoil or a whole airplane, or the flow
of air around a car. Also in many instances in geophysical fluid
mechanics, like the interface of air and earth, or air and ocean.
This self-contained monograph is devoted to the study of certain
classes of singular perturbation problems mostly related to
thermic, fluid mechanics and optics and where mostly elliptic or
parabolic equations in a bounded domain are considered. This book
is a fairly unique resource regarding the rigorous mathematical
treatment of boundary layer problems. The explicit methodology
developed in this book extends in many different directions the
concept of correctors initially introduced by J. L. Lions, and in
particular the lower- and higher-order error estimates of
asymptotic expansions are obtained in the setting of functional
analysis. The review of differential geometry and treatment of
boundary layers in a curved domain is an additional strength of
this book. In the context of fluid mechanics, the outstanding open
problem of the vanishing viscosity limit of the Navier-Stokes
equations is investigated in this book and solved for a number of
particular, but physically relevant cases. This book will serve as
a unique resource for those studying singular perturbations and
boundary layer problems at the advanced graduate level in
mathematics or applied mathematics and may be useful for
practitioners in other related fields in science and engineering
such as aerodynamics, fluid mechanics, geophysical fluid mechanics,
acoustics and optics.
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