The reconstruction of a wave equation from one side measurement

DOI10.1016/J.WAVEMOTI.2020.102547arXiv1901.02138MaRDI QIDQ6312135

Publication date: 7 January 2019

Abstract: We are concerned with the reconstruction of a one dimensional wave equation, where the potential is known in a neighborhood of one of the end points of the boundary. We show then the sought potential can be determined by one single measurement of the solution at that end. We also show that the solution can be evaluated at the other end without the need of solving the wave the equation.

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Inverse problems for PDEs (35R30) Inverse problems involving ordinary differential equations (34A55)

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