Identification of a source in a fractional wave equation from a boundary measurement

We deal with an inverse source problem in a time-fractional wave equation. The time-dependent source term is reconstructed using the additional non-invasive measurement in the form of integral over a part of the boundary. We look for the solution and the source term obeying the variational formulati...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2019-03, Vol.349, p.172-186
Main Authors: Šišková, K., Slodička, M.
Format: Article
Language:English
Subjects:
Boundary measurement
Convergence
Inverse source problem
Reconstruction
Time discretization
Time-fractional wave equation
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Summary:We deal with an inverse source problem in a time-fractional wave equation. The time-dependent source term is reconstructed using the additional non-invasive measurement in the form of integral over a part of the boundary. We look for the solution and the source term obeying the variational formulation and the equation obtained from applying the measurement on the equation. Using the Rothe method the existence of the solution is proven. The uniqueness is shown in appropriate spaces and some numerical experiments are presented.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2018.09.020