Korpela, J;
Lassas, M;
Oksanen, L;
(2019)
Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation.
Inverse Problems and Imaging
, 13
(3)
pp. 575-596.
10.3934/ipi.2019027.
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Abstract
An inverse boundary value problem for the 1+1 dimensional wave equation ( ∂ 2 t − c ( x ) 2 ∂ 2 x ) u ( x , t ) = 0 , x ∈ R + is considered. We give a discrete regularization strategy to recover wave speed c ( x ) when we are given the boundary value of the wave, u ( 0 , t ) , that is produced by a single pulse-like source. The regularization strategy gives an approximative wave speed ˜ c , satisfying a Hölder type estimate ∥ ˜ c − c ∥ ≤ C ϵ γ , where ϵ is the noise leve
| Type: | Article |
|---|---|
| Title: | Discrete regularization and convergence of the inverse problem for 1+1 dimensional wave equation |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.3934/ipi.2019027 |
| Publisher version: | http://dx.doi.org/10.3934/ipi.2019027 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Inverse problem, regularization theory, wave equation, discretization. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10072536 |
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