Prof. Sergei Avdonin, Univ. of Alaska

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Prof. Sergei Avdonin, Univ. of Alaska

Spectral and Dynamical Inverse Boundary Problems

The boundary control (BC) method in inverse theory is based on deep connections between controllability and identifiability of dynamical systems. In this talk we describe the main ideas of this method, as well as its main features, such as locality. This method was developed for solving dynamical inverse problems, and it allows also to recover spectral properties of the underlying systems and to solve spectral inverse problems.

Another ramification of the BC method is the leaf-peeling method for solving inverse problems for differential equations on graphs. The inverse problem consists in reconstructing the metric graph (topology and lengths of edges), differential operator on its edges and matching conditions at the internal vertices from spectral or dynamical data. The leaf-peeling method combines spectral and dynamical approaches to inverse problems and develops a constructive procedure for the recovery of graphs parameters. This procedures is recursive — it allows recalculating the inverse data from the original graph to smaller graphs.

A new approach to source identification problems closely related to boundary control problems will also be discussed.