Identifiability and Stability of Boundaries in a Supercritical Free Surface Flow

Abstract

In this paper, we have studied a problem of identifiability of boundaries and stability of the solutions for the direct and the inverse problem concerning a supercritical and irrotational ow of an inviscid uid over an obstacle which lies on the bottom of a channel. The identifiability of the solution means its uniqueness when it exists. The stability is studied in the sense that for the direct problem and the inverse one, we study the variation of the obtained geometry for a little perturbation of the bottom or of the free surface. The proofs of the theorems are based on Holmgren theorem and the mean value theorem. The stability obtained is linear.