Classical and Stochastic Laplacian Growth

• Main Authors: Gustafsson, Björn (Author), Teodorescu, Razvan (Author), Vasil’ev, Alexander (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2014.
• Series: Advances in Mathematical Fluid Mechanics,
• Subjects: Mathematics.; Functions of complex variables.; Numerical analysis.; Mathematical physics.; Mathematical Physics.; Numerical Analysis.; Functions of a Complex Variable.

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 theoreti...

Table of Contents:

• 1 Introduction and Background
• 2 Rational and Other Explicit Strong Solutions
• 3 Weak Solutions and Related Topics
• 4 Geometric Properties
• 5 Capacities and Isoperimetric Inequalities
• 6 Laplacian Growth and Random Matrix Theory
• 7 Integrability and Moments
• 8 Shape Evolution and Integrability
• 9 Stochastic Löwner and Löwner-Kufarev Evolution
• References
• List of Symbols
• Index.