Determining a boundary coefficient in a dissipative wave equation: Uniqueness and directional lipschitz stability
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Publication:6259994
DOI10.1007/S00233-016-9845-2arXiv1503.04528MaRDI QIDQ6259994
Publication date: 16 March 2015
Abstract: We are concerned with the problem of determining the damping boundary coefficient appearing in a dissipative wave equation from a single boundary measurement. We prove that the uniqueness holds at the origin provided that the initial condition is appropriately chosen. We show that the choice of the initial condition leading to uniqueness is related to a fine version of unique continuation property for elliptic operators. We also establish a Lipschitz directional stability estimate at the origin, which is obtained by a linearization process.
Initial-boundary value problems for second-order hyperbolic equations (35L20) Inverse problems for PDEs (35R30)
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