Inverse problems for one-dimensional fluid-solid interaction models

TL;DR

This paper investigates inverse problems for a one-dimensional fluid-solid interaction model governed by Burgers equation, focusing on determining the interface shape from boundary data, with results on uniqueness and stability.

Contribution

It establishes uniqueness and stability results for the inverse interface problem using Carleman and interpolation inequalities, adapting lateral estimates for the Burgers-based model.

Findings

Proves uniqueness of the interface shape from boundary data.

Provides conditional stability estimates for the inverse problem.

Employs Carleman inequalities to derive stability results.

Abstract

We consider a one-dimensional fluid-solid interaction model governed by the Burgers equation with a time varying interface. We discuss on the inverse problem of determining the shape of the interface from Dirichlet and Neumann data at one end point of the spatial interval. In particular, we establish uniqueness results and some conditional stability estimates. For the proofs, we use and adapt some lateral estimates that, in turn, rely on appropriate Carleman and interpolation inequalities.