Identifiability and stability of boundaries in a supercritical free surface

作者：Teniou Djamel Eddine^*; Ait Yahia Rachida; Hernane Dahbia

来源：Revista Matematica Complutense, 2008, 21(1): 61-73.

• inverse problem
• free boundary
• identifiability
• stability

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 flow of an inviscid fluid 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.

• 出版日期2008