Laplacian growth on branched Riemann surfaces / Björn Gustafsson, Yu-Lin Lin.
Gustafsson, Björn, 1947- author.; Lin, Yu-Lin, author.
2021
QA911
Available Online

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Title Laplacian growth on branched Riemann surfaces / Björn Gustafsson, Yu-Lin Lin.
Author Gustafsson, Björn, 1947- author.
ISBN 9783030698638 (electronic bk.)
3030698637 (electronic bk.)
9783030698621
3030698629
DOI https://doi.org/10.1007/978-3-030-69863-8
Published Cham, Switzerland : Springer, [2021]
Language English
Description 1 online resource
Item Number 10.1007/978-3-030-69863-8 doi
Call Number QA911
Dewey Decimal Classification 532/.053
Summary This book studies solutions of the Polubarinova-Galin and Löwner-Kufarev equations, which describe the evolution of a viscous fluid (Hele-Shaw) blob, after the time when these solutions have lost their physical meaning due to loss of univalence of the mapping function involved. When the mapping function is no longer locally univalent interesting phase transitions take place, leading to structural changes in the data of the solution, for example new zeros and poles in the case of rational maps. This topic intersects with several areas, including mathematical physics, potential theory and complex analysis. The text will be valuable to researchers and doctoral students interested in fluid dynamics, integrable systems, and conformal field theory.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed April 14, 2021).
Added Author Lin, Yu-Lin, author.
Series Lecture notes in mathematics (Springer-Verlag) ; 2287. 0075-8434
Available in Other Form Print version: 9783030698621
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Introduction
The Polubarinova-Galin and Löwner-Kufarev Equations
Weak Solutions and Balayage
Weak and Strong Solutions on Riemann Surfaces
Global Simply Connected Weak Solutions
General Structure of Rational Solutions
Examples
Moment Coordinates and the String Equation
Hamiltonian Descriptions of General Laplacian Evolutions
The String Equation for Some Rational Functions.

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