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An inverse problem for the wave equation. (English) Zbl 1279.34020

Summary: In the first part of this article, we show that we can recover the coefficient \(q\) in the one-dimensional wave equation from a finite number of special lateral measurements. Moreover, if some estimates on the size of \(q\) are available, then \(q\) can be recovered from a single boundary measurement. In the second part we treat the multidimensional case and show how we can reconstruct the coefficient \(q\) from a sequence of boundary measurements taken at one point only.

MSC:

34A55 Inverse problems involving ordinary differential equations
34B24 Sturm-Liouville theory
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
35L05 Wave equation
35R30 Inverse problems for PDEs
42C15 General harmonic expansions, frames
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References:

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