Overview
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.
Full Product Details
Author: Björn Gustafsson ,
Razvan Teodorescu ,
Alexander Vasil’ev
Publisher: Birkhauser Verlag AG
Imprint: Birkhauser Verlag AG
Edition: 2014 ed.
Dimensions:
Width: 15.50cm
, Height: 1.90cm
, Length: 23.50cm
Weight: 0.664kg
ISBN: 9783319082868
ISBN 10: 3319082868
Pages: 317
Publication Date: 04 December 2014
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: In Print
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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)
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)
“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)
