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Conformal and Potential Analysis in Hele-Shaw Cell [electronic resource] /by Björn Gustafsson, Alexander Vasil’ev.

by Gustafsson, Björn [author.]; Vasil’ev, Alexander [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Advances in Mathematical Fluid Mechanics: Publisher: Basel : Birkhäuser Basel, 2006.Description: X, 231 p. online resource.ISBN: 9783764377045.Subject(s): Mathematics | Differential equations, partial | Potential theory (Mathematics) | Thermodynamics | Mathematics | Partial Differential Equations | Potential Theory | Mechanics, Fluids, ThermodynamicsDDC classification: 515.353 Online resources: Click here to access online
Contents:
and Background -- Explicit Strong Solutions -- Weak Solutions and Balayage -- Geometric Properties -- Capacities and Isoperimetric Inequalities -- General Evolution Equations -- Hele-Shaw Evolution and Strings.
In: Springer eBooksSummary: This monograph aims at giving a presentation of recent and new ideas that arise from the problems of planar fluid dynamics and which are interesting from the point of view of geometric function theory and potential theory. In particular, this book is concerned with geometric problems for Hele-Shaw flows. Also Hele-Shaw flows on parameter spaces (e.g., the Teichmüller space) are treated and connections with string theory are revealed. Ultimately, the interaction between several branches of complex and potential analysis, and planar fluid mechanics is discussed. For most parts of this book the background provided by graduate courses in real and complex analysis, in particular, the theory of conformal mappings and in fluid mechanics is assumed. There are some historical remarks concerning the people that have contributed to the topic. The book is as self-contained as possible.
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and Background -- Explicit Strong Solutions -- Weak Solutions and Balayage -- Geometric Properties -- Capacities and Isoperimetric Inequalities -- General Evolution Equations -- Hele-Shaw Evolution and Strings.

This monograph aims at giving a presentation of recent and new ideas that arise from the problems of planar fluid dynamics and which are interesting from the point of view of geometric function theory and potential theory. In particular, this book is concerned with geometric problems for Hele-Shaw flows. Also Hele-Shaw flows on parameter spaces (e.g., the Teichmüller space) are treated and connections with string theory are revealed. Ultimately, the interaction between several branches of complex and potential analysis, and planar fluid mechanics is discussed. For most parts of this book the background provided by graduate courses in real and complex analysis, in particular, the theory of conformal mappings and in fluid mechanics is assumed. There are some historical remarks concerning the people that have contributed to the topic. The book is as self-contained as possible.

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