Inverse scattering problem for quasi-linear perturbation of the biharmonic operator on the line
Tyni, Teemu; Serov, Valery (2019-02-28)
Teemu Tyni, Valery Serov. Inverse scattering problem for quasi-linear perturbation of the biharmonic operator on the line. Inverse Problems & Imaging, 2019, 13 (1) : 159-175. doi: 10.3934/ipi.2019009
Inverse Problems & Imaging © 2019 Published by AIMS. All rights reserved.
https://rightsstatements.org/vocab/InC/1.0/
https://urn.fi/URN:NBN:fi-fe2019040311030
Tiivistelmä
Abstract
We consider an inverse scattering problem of recovering the unknown coefficients of quasi-linearly perturbed biharmonic operator on the line. 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 that the inverse Born approximation can be used to recover some essential information about the unknown coefficients from the knowledge of the reflection coefficient. This information is the jump discontinuities and the local singularities of the coefficients.
Kokoelmat
- Avoin saatavuus [31926]