Overview
- Combines features of an in-depth monograph and a highly instructive survey of state-of-the-art techniques and results
- Addresses graduate students and researchers in analysis and its applications
- Contains plenty of graphical representations and concrete problems?
Part of the book series: Advances in Mathematical Fluid Mechanics (AMFM)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Löwner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive bibliography covering over twelve decades of results and an introduction rich in historical and biographical details complement the eight main chapters of this monograph.
Given its systematic and consistent notation and background results, this book provides a self-contained resource. It is accessible to a wide readership, from beginner graduate students to researchers from various fields in natural sciences and mathematics.
Reviews
“This monograph on Laplacian growth is ideal for experts seeking a reference book (with an extensive bibliography spanning almost 600 references) as well as for interested researchers that are new to the subject. … the text does an impressive job covering such an extensive range of topics while providing an expert treatment that is also fairly accessible for students.” (Erik Eugene Lundberg, Mathematical Reviews, November, 2015)
Authors and Affiliations
Bibliographic Information
Book Title: Classical and Stochastic Laplacian Growth
Authors: Björn Gustafsson, Razvan Teodorescu, Alexander Vasil’ev
Series Title: Advances in Mathematical Fluid Mechanics
DOI: https://doi.org/10.1007/978-3-319-08287-5
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-08286-8Published: 04 December 2014
Softcover ISBN: 978-3-319-37639-4Published: 22 September 2016
eBook ISBN: 978-3-319-08287-5Published: 14 November 2014
Series ISSN: 2297-0320
Series E-ISSN: 2297-0339
Edition Number: 1
Number of Pages: XIV, 317
Number of Illustrations: 39 b/w illustrations, 13 illustrations in colour
Topics: Mathematical Physics, Numerical Analysis, Functions of a Complex Variable