Softcover ISBN:  9780821870020 
Product Code:  ULECT/3 
72 pp 
List Price:  $22.00 
MAA Member Price:  $19.80 
AMS Member Price:  $17.60 
Electronic ISBN:  9780821832189 
Product Code:  ULECT/3.E 
72 pp 
List Price:  $20.00 
MAA Member Price:  $18.00 
AMS Member Price:  $16.00 

Book DetailsUniversity Lecture SeriesVolume: 3; 1992MSC: Primary 30; 31; 58; 76;
This book concerns the problem of evolution of a round oil spot surrounded by water when oil is extracted from a well inside the spot. It turns out that the boundary of the spot remains an algebraic curve of degree four in the course of evolution. This curve is the image of an ellipse under a reflection with respect to a circle. Since the 1940s, work on this problem has led to generalizations of the reflection property and methods for constructing explicit solutions. More recently, the results have been extended to multiply connected domains. This text discusses this topic and other recent work in the theory of fluid flows with a moving boundary. Problems are included at the end of each chapter, and there is a list of open questions at the end of the book.
ReadershipAdvanced undergraduates, graduate students, and others interested in integrable systems and fluid mechanics.

Table of Contents

Chapters

Chapter 1. Mathematical model

Chapter 2. First integrals of boundary motion

Chapter 3. Algebraic solutions

Chapter 4. Contraction of a gas bubble

Chapter 5. Evolution of a multiply connected domain

Chapter 6. Evolution with topological transformations

Chapter 7. Contraction problem on surfaces

Answers and clues to the problems

A few open questions


Reviews

The book is well written.
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This book concerns the problem of evolution of a round oil spot surrounded by water when oil is extracted from a well inside the spot. It turns out that the boundary of the spot remains an algebraic curve of degree four in the course of evolution. This curve is the image of an ellipse under a reflection with respect to a circle. Since the 1940s, work on this problem has led to generalizations of the reflection property and methods for constructing explicit solutions. More recently, the results have been extended to multiply connected domains. This text discusses this topic and other recent work in the theory of fluid flows with a moving boundary. Problems are included at the end of each chapter, and there is a list of open questions at the end of the book.
Advanced undergraduates, graduate students, and others interested in integrable systems and fluid mechanics.

Chapters

Chapter 1. Mathematical model

Chapter 2. First integrals of boundary motion

Chapter 3. Algebraic solutions

Chapter 4. Contraction of a gas bubble

Chapter 5. Evolution of a multiply connected domain

Chapter 6. Evolution with topological transformations

Chapter 7. Contraction problem on surfaces

Answers and clues to the problems

A few open questions

The book is well written.
Mathematical Reviews