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Boundary control, wave field continuation and inverse problems for the wave equation. (English) Zbl 0768.35077

Summary: We consider the problem of the wave field continuation and recovering of coefficients for the wave equation in a bounded domain in \(\mathbb{R}^ n\), \(n>1\). The inverse data is a response operator mapping Neumann boundary data into Dirichlet ones. The reconstruction procedure is local. This means that, observing boundary response for larger times, we may recover coefficients deeper in the domain. The approach is based upon ideas and results of the boundary control theory, yielding some natural multidimensional analogs of the classical Gel’fand-Levitan-Krein equations.

MSC:

35R30 Inverse problems for PDEs
93C20 Control/observation systems governed by partial differential equations
35B37 PDE in connection with control problems (MSC2000)
35L05 Wave equation
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