We consider the following inverse problem: Suppose a (1 + 1)-dimensional wave equation on R+ with zero initial conditions is excited with a Neumann boundary data modelled as a white noise process. Given also the Dirichlet data at the same point, determine the unknown first order coefficient function of the system. The inverse problem is then solved by showing that correlations of the boundary data determine the Neumann-to-Dirichlet operator in the sense of distributions, which is known to uniquely identify the coefficient. The model has potential applications in acoustic measurements of internal cross-sections of fluid pipes such as pressurised water supply pipes and vocal tract shape determination. This talk is based on a joint-work with Emilia Blåsten, Antti Kujanpää and Tapio Helin (LUT), and Lauri Oksanen (Helsinki).

In this talk we address the issue of stability for the first order perturbation of the biharmonic operator from partial data, in a bounded domain of dimension three or higher. Specifically, we shall consider two partial data settings: (1) Assuming that the inaccessible portion of the boundary is flat, and we have knowledge of the Dirichlet-to-Neumann map on the complement. (2) Assuming that the perturbations are known in a neighborhood of the boundary, measurements are performed only on arbitrarily small open subsets of the boundary. In both settings we obtain log type stability estimates. Part of this talk is based on a joint work with Salem Selim.

https://sites.uci.edu/inverse/

https://sites.uci.edu/inverse/

In this talk I will survey the classical Boundary Control method, originally developed by Belishev and Kurylev, which can be used to reduce an inverse problem for a hyperbolic equation, on a complete Riemannian manifold, to a purely geometric problem involving the so-called travel time data. For each point in the manifold the travel time data contains the distance function from this point to any point in a fixed a priori known closed observation set. If the Riemannian manifold is closed then the observation set is a closure of an open and bounded set, and in the case of a manifold with boundary the observation set is an open subset of the boundary. We will survey many known uniqueness and stability results related to the travel time data.