Abstract
We consider an inverse scattering problem of recovering the unknown coefficients of a quasi-linearly perturbed biharmonic operator in the three-dimensional case. These unknown complex-valued coefficients are assumed to satisfy some regularity conditions on their nonlinearity, but they can be discontinuous or singular in their space variable. We prove Saito’s formula and uniqueness theorem of recovering some essential information about the unknown coefficients from the knowledge of the high frequency scattering amplitude.
Funding source: Academy of Finland
Award Identifier / Grant number: 312123
Funding statement: This work was supported by the Academy of Finland (application number 312123, the Centre of Excellence of Inverse Modelling and Imaging 2018-2025) and by Moscow Centre of Fundamental and Applied Mathematics – MSU, Russia.
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