摘要：AbstractWe consider control and inverse problems for the wave and Schrödinger equations on metric graphs, including graphs with cycles. We find conditions for the exact controllability of the wave equation on graphs. The complete solution of the inverse problem consists of reconstructing the graph’s topology, the lengths of all edges and coefficients of the equations. We prove the uniqueness theorem and propose a stable identification algorithm, which is based on the leaf peeling method proposed earlier for graphs without cycles (trees).
