In this talk we will first briefly review some geometric inverse problems we have studied for the one-dimensional heat, wave and Burgers equations. Then, we will consider a one-dimensional fluid-solid interaction model governed by the Burgers equation with a time varying interface. This is a preliminary simplified version of other more complicate and more realistic models in higher dimensions. We will see the results we have obtained for 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 will show uniqueness results and some conditional stability estimates. For the proofs, it will be seen that some lateral estimates have been used and adapted, which rely on appropriate Carleman and interpolation inequalities.

Zoom meeting: link