Laplacian growth on branched Riemann surfaces / Björn Gustafsson, Yu-Lin Lin.

Format:

Book

Author/Creator:

Gustafsson, Björn, 1947- author.

Lin, Yu-Lin (Associate lecturer), author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2287.

Lecture notes in mathematics, 0075-8434 ; volume 2287

Language:

English

Subjects (All):

Fluid dynamics--Mathematics.

Fluid dynamics.

Geometric function theory.

Laplacian matrices.

Riemann surfaces.

Genre:

Textbooks.

Physical Description:

xii, 154 pages : illustrations (some color) ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2021]

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.

Contents:

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.

Notes:

Includes bibliographical references and index.

Includes bibliographical references (pages 147-152) and index.

ISBN:

9783030698621

3030698629

OCLC:

1250007731