The stability for an inverse problem of bottom recovering in water-waves. (23rd October 2020)

• Record Type: Journal Article
• Authors: Lecaros, R; López-Ríos, J; Ortega, J H; Zamorano, S
• Is Part Of: Inverse problems. Volume 36:Number 11(2020)
• Publication Date: 2020-10-23
• Subjects: free boundary value problems -- water-waves equations -- geometric inverse problems -- stability -- size estimate -- non-local operators; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abafee
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water-waves. We found upper and lower bounds for the size of the region enclosed between two different bottoms, in terms of Neumann and/or Dirichlet data on the free surface. Starting from the general water-waves system in bounded domains with side walls, we manage to formulate the problem in terms of the Dirichlet to Neumann operator and thus, as an elliptic problem in a bounded domain with Neumann homogeneous condition on the rigid boundary. Then we study the properties of the Dirichlet to Neumann map and analyze the called method of size estimation.