ORIGINAL PAPERS

Stable Determination of the Initial Data in an IBVP for the Wave Equation Outside a Non-trapping Obstacle

  • Mourad Choulli
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  • Université de Lorraine, Nancy, France

Received date: 2024-01-04

  Revised date: 2024-03-25

  Online published: 2026-02-11

Abstract

We establish a double logarithmic stability inequality for the problem of determining the initial data in an IBVP for the wave equation outside a non-trapping obstacle from two localized measurements.

Cite this article

Mourad Choulli . Stable Determination of the Initial Data in an IBVP for the Wave Equation Outside a Non-trapping Obstacle[J]. Communications on Applied Mathematics and Computation, 2026 , 8(1) : 87 -93 . DOI: 10.1007/s42967-024-00407-9

References

[1] Choulli, M.: Uniqueness of continuation for semilinear elliptic equations. arXiv:2208.08378 (2022)
[2] Finch, D., Hickmann, K.S.: Transmission eigenvalues and thermoacoustic tomography. Inverse Probl. 29(10), 104016 (2013)
[3] Kian, Y., Uhlamnn, G.: Determination of the sound speed and an initial source in photoacoustic tomography. arXiv:2302.03457 (2023)
[4] Liu, H., Uhlmann, G.: Determining both sound speed and internal source in thermo- and photo-acoustic tomography. Inverse Probl. 31(10), 105005 (2015)
[5] Morawetz, C.S., Ralston, J.V., Strauss, W.A.: Decay of solutions of the wave equation outside nontrapping obstacles. Commun. Pure Appl. Math. 30(4), 447-508 (1977)
[6] Stefanov, P., Uhlmann, G.: Thermoacoustic tomography with variable sound speed. Inverse Probl. 25(7), 075011 (2009)
[7] Stefanov, P., Uhlmann, G.: Thermoacoustic tomography arising in brain imaging. Inverse Probl. 27(4), 045004 (2011)
[8] Stefanov, P., Uhlmann, G.: Recovery of a source term or a speed with one measurement and applications. Trans. Am. Math. Soc. 365(11), 5737-5758 (2013)
[9] Stefanov, P., Uhlmann, G.: Instability of the linearized problem in multiwave tomography of recovery both the source and the speed. Inverse Probl. Imaging 7(4), 1367-1377 (2013)
[10] Tucsnak, M., Weiss, G.: Observation and Control for Operator Semigroups. Birkhäuser Verlag, Basel (2009)
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