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Why the Boundary of a Round Drop Becomes a Curve of Order Four

A. N. Varchenko University of North Carolina, Chapel Hill, Chapel Hill, NC
P. I. Etingof Harvard University, Cambridge, MA
Available Formats:
Softcover ISBN: 978-0-8218-7002-0
Product Code: ULECT/3
72 pp
List Price: $22.00 MAA Member Price:$19.80
AMS Member Price: $17.60 Electronic ISBN: 978-0-8218-3218-9 Product Code: ULECT/3.E 72 pp List Price:$20.00
MAA Member Price: $18.00 AMS Member Price:$16.00
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List Price: $33.00 MAA Member Price:$29.70
AMS Member Price: $26.40 Click above image for expanded view Why the Boundary of a Round Drop Becomes a Curve of Order Four A. N. Varchenko University of North Carolina, Chapel Hill, Chapel Hill, NC P. I. Etingof Harvard University, Cambridge, MA Available Formats:  Softcover ISBN: 978-0-8218-7002-0 Product Code: ULECT/3 72 pp  List Price:$22.00 MAA Member Price: $19.80 AMS Member Price:$17.60
 Electronic ISBN: 978-0-8218-3218-9 Product Code: ULECT/3.E 72 pp
 List Price: $20.00 MAA Member Price:$18.00 AMS Member Price: $16.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$33.00
MAA Member Price: $29.70 AMS Member Price:$26.40
• Book Details

University Lecture Series
Volume: 31992
MSC: 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.

• 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.

Mathematical Reviews
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Volume: 31992
MSC: 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.

• 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
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