Laplacian Growth on Branched Riemann Surfaces
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Beschreibung
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.
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.
Explores unsolved problems and new directions related to domain evolutions on Riemann surfaces Presents potentially fruitful ideas around the ill-posed suction problem Gives elementary, but intriguing, examples involving only polynomials and rational functions
Autor*in
Björn Gustafsson
Themen in »Laplacian Growth on Branched Riemann Surfaces«
Branched Riemann Surface Computational Fluid Dynamics Conformal Analysis Fluid Flow Function Theory Hele-Shaw Flow Integrable System Laplacian Growth Moving Boundary Problem String Equation
Stimmen zu »Laplacian Growth on Branched Riemann Surfaces«
“This interesting book is devoted to the Laplacian growth on Riemann surfaces. … This book is a valuable contribution to the modern theory of Laplacian growth. It contains many useful and interesting results, together with a rigorous analysis of all treated problems.” (Mirela Kohr, zbMATH 1526.30032, 2024)
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