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Geometric properties of the solutions of a Hele-Shaw type equation

Authors: Konstantin Kornev and Alexander Vasil'ev
Journal: Proc. Amer. Math. Soc. 128 (2000), 2683-2685
MSC (1991): Primary 35Q35; Secondary 30C45
Published electronically: February 25, 2000
MathSciNet review: 1664386
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Abstract: This article deals with the application of the methods of geometric function theory to the investigation of the free boundary problem for the equation describing flows in an unbounded simply-connected plane domain. We prove the invariance of some geometric properties of a moving boundary.

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Additional Information

Konstantin Kornev
Affiliation: Institute of Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

Alexander Vasil'ev
Affiliation: Departamento de Matemáticas, Universidad de los Andes, Bogotá, Colombia

Keywords: Free boundary, Hele-Shaw equation, convex function in the positive direction
Received by editor(s): May 26, 1998
Received by editor(s) in revised form: October 27, 1998
Published electronically: February 25, 2000
Additional Notes: The authors were supported in part by the Russian Foundation for Basic Research, Grants #98-01-00842, #98-15-96002.
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society