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Why the Boundary of a Round Drop Becomes a Curve of Order Four
Aleksandr Nikolaevich VarchenkoPavel I. Etingof
出版American Mathematical Soc., 1992
主題Mathematics / GeneralMathematics / Differential Equations / General
ISBN08218700259780821870020
URLhttp://books.google.com.hk/books?id=LcAFCAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋This monograph 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.