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Abstract and Applied Analysis
Volume 2005, Issue 2, Pages 159-171
http://dx.doi.org/10.1155/AAA.2005.159

A study of the inverse of a free-surface problem

Faculté de Mathématiques, Université des Sciences et de la Technologie Houari Boumediene (USTHB), El Alia, Alger, Bab-Ezzouar BP 32, 16123, Algeria

Received 18 February 2004

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove the existence of an obstacle lying on the bottom of an infinite channel inducing a surface on the upper bound of the fluid domain. This problem is the inverse of the free-surface problem flow which has been studied by several authors. We use the implicit function theorem to establish the existence of the solution of the problem.