University Lecture Series 1992; 72 pp; softcover Volume: 3 ISBN10: 0821870025 ISBN13: 9780821870020 List Price: US$19 Member Price: US$15.20 Order Code: ULECT/3
 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. Readership Advanced undergraduates, graduate students, and others interested in integrable systems and fluid mechanics. Reviews "The book is well written."  Mathematical Reviews Table of Contents  Mathematical model
 First integrals of boundary motion
 Algebraic solutions
 Contraction of a gas bubble
 Evolution of a multiply connected domain
 Evolution with topological transformations
 Contraction problem on surfaces
