|
Showing 1 - 2 of
2 matches in All Departments
This is the first volume of a series of books that will describe
current advances and past accompli shments of mathemat i ca 1
aspects of nonlinear sCience taken in the broadest contexts. This
subject has been studied for hundreds of years, yet it is the topic
in whi ch a number of outstandi ng di scoveri es have been made in
the past two decades. Clearly, this trend will continue. In fact,
we believe some of the great scientific problems in this area will
be clarified and perhaps resolved. One of the reasons for this
development is the emerging new mathematical ideas of nonlinear
science. It is clear that by looking at the mathematical structures
themselves that underlie experiment and observation that new vistas
of conceptual thinking lie at the foundation of the unexplored area
in this field. To speak of specific examples, one notes that the
whole area of bifurcation was rarely talked about in the early
parts of this century, even though it was discussed mathematically
by Poi ncare at the end of the ni neteenth century. I n another di
rect ion, turbulence has been a key observation in fluid dynamics,
yet it was only recently, in the past decade, that simple computer
studies brought to light simple dynamical models in which chaotic
dynamics, hopefully closely related to turbulence, can be observed.
Nonlinearity and Functional Analysis is a collection of lectures
that aim to present a systematic description of fundamental
nonlinear results and their applicability to a variety of concrete
problems taken from various fields of mathematical analysis. For
decades, great mathematical interest has focused on problems
associated with linear operators and the extension of the
well-known results of linear algebra to an infinite-dimensional
context. This interest has been crowned with deep insights, and the
substantial theory that has been developed has had a profound
influence throughout the mathematical sciences. This volume
comprises six chapters and begins by presenting some background
material, such as differential-geometric sources, sources in
mathematical physics, and sources from the calculus of variations,
before delving into the subject of nonlinear operators. The
following chapters then discuss local analysis of a single mapping
and parameter dependent perturbation phenomena before going into
analysis in the large. The final chapters conclude the collection
with a discussion of global theories for general nonlinear
operators and critical point theory for gradient mappings. This
book will be of interest to practitioners in the fields of
mathematics and physics, and to those with interest in conventional
linear functional analysis and ordinary and partial differential
equations.
|
You may like...
Morgan
Kate Mara, Jennifer Jason Leigh, …
Blu-ray disc
(1)
R70
Discovery Miles 700
Tenet
John David Washington, Robert Pattinson
Blu-ray disc
(1)
R54
Discovery Miles 540
|
Email address subscribed successfully.
A activation email has been sent to you.
Please click the link in that email to activate your subscription.