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.
R. Ait Yahia-Djouadi. D. Hernane-Boukari. D. Teniou. "A study of the inverse of a free-surface problem." Abstr. Appl. Anal. 2005 (2) 159 - 171, 28 April 2005. https://doi.org/10.1155/AAA.2005.159