Classical and Stochastic Laplacian Growth

  • Björn Gustafsson
  • Razvan Teodorescu
  • Alexander Vasil’ev
Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Björn Gustafsson, Razvan Teodorescu, Alexander Vasil’ev
    Pages 1-46
  3. Björn Gustafsson, Razvan Teodorescu, Alexander Vasil’ev
    Pages 47-82
  4. Björn Gustafsson, Razvan Teodorescu, Alexander Vasil’ev
    Pages 83-126
  5. Björn Gustafsson, Razvan Teodorescu, Alexander Vasil’ev
    Pages 127-162
  6. Björn Gustafsson, Razvan Teodorescu, Alexander Vasil’ev
    Pages 163-186
  7. Björn Gustafsson, Razvan Teodorescu, Alexander Vasil’ev
    Pages 187-210
  8. Björn Gustafsson, Razvan Teodorescu, Alexander Vasil’ev
    Pages 211-229
  9. Björn Gustafsson, Razvan Teodorescu, Alexander Vasil’ev
    Pages 231-261
  10. Björn Gustafsson, Razvan Teodorescu, Alexander Vasil’ev
    Pages 263-275
  11. Back Matter
    Pages 277-317

About this book

Introduction

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.

Keywords

Laplacian growth model balayage free-boundary problems inverse-moment problem random matrices stochastic process

Authors and affiliations

  • Björn Gustafsson
    • 1
  • Razvan Teodorescu
    • 2
  • Alexander Vasil’ev
    • 3
  1. 1.Department of MathematicsKTH Royal Institute of TechnologyStockholmSweden
  2. 2.Department of MathematicsUniversity of South FloridaTampaUSA
  3. 3.Department of MathematicsUniversity of BergenBergenNorway

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-08287-5
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-08286-8
  • Online ISBN 978-3-319-08287-5
  • Series Print ISSN 2297-0320
  • Series Online ISSN 2297-0339
  • About this book