Laplacian Growth on Branched Riemann Surfaces

The 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. When the mapping function is no longer locally univalent,interesting phase transitions take place,leading to structural changes in the data of the solution. This topic intersects with mathematical physics,potential theory,and complex analysis.

Format: Paperback / softback
Length: 156 pages
Publication date: 23 March 2021
Publisher: Springer Nature Switzerland AG

This book delves into the study of solutions to the Polubarinova-Galin and Löwner-Kufarev equations, which shed light on the evolution of a viscous fluid (Hele-Shaw) blob after it loses its physical significance due to the loss of univalence in the mapping function involved. As the mapping function becomes non-locally univalent, intriguing phase transitions occur, resulting in structural alterations in the solution's data. These transitions lead to the emergence of new zeros and poles, particularly in the case of rational maps. This research area intersects with various fields such as mathematical physics, potential theory, and complex analysis, making it of significant interest to scholars and doctoral students engaged in fluid dynamics, integrable systems, and conformal field theory. The insights gained from this book will be invaluable to those seeking to advance their understanding of these complex mathematical phenomena.

Weight: 276g
Dimension: 157 x 234 x 15 (mm)
ISBN-13: 9783030698621
Edition number: 1st ed. 2021