Kielhöfer, H., University of Augsburg, Germany
Bifurcation Theory
An Introduction with
Applications to PDEs Second Edition
Springer Verlag
2011, 398 p. 48 illus. Hardcover
In the past three decades, bifurcation theory has
matured into a wellestablished and vibrant branch of mathematics. This book gives a unified presentation
in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser
known results. It covers both the local and global theory of oneparameter bifurcations for operators
acting in infinitedimensional Banach spaces, and shows how to apply the theory to problems involving
partial differential equations. In addition to existence, qualitative properties such as stability and
nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important
reference for mathematicians, physicists, and theoreticallyinclined engineers working in bifurcation
theory and its applications to partial differential equations.
The second edition is substantially and formally revised and new material is added. Among this is bifurcation with a twodimensional kernel with applications, the buckling of the Eulder rod, the appearance of Taylor vortices, the singular limit process of the CahnHilliard model, and an application of this method to more complicated nonconvex variational problems.
Contents: Introduction. Local Theory.
Global Theory. Applications.
Series:
Applied Mathematical Sciences. Vol.. 156
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