Applicable Analysis wants to become a leading journal for publishing papers on all mathematical aspects of Inverse Problems. This is why, the Editorial Board has decided to dedicate two special issues to this discipline.
The interest of the mathematical community in Inverse Problems is rapidly growing due to a large number of applications. In general, an inverse problem is a problem of an estimate of a property of an unknown medium of interest, given measurements of an output signal. Since this signal is propagating through this medium, it should carry a signature of that property. That ‘magic’ property is usually spatially distributed. Some examples include the speed of sound in the case of acoustic wave propagation, dielectric function and/or the conductivity in the case of electromagnetic waves propagation, as well as absorption coefficient of light in the case of light propagation through a biological medium. Already these limited examples tell one that applications of Inverse Problems include geophysics when the Earth is probed by either acoustical or electromagnetic waves, material science, medical optical imaging and many others. Historically the entire discipline of Inverse Problems was originated due to needs of geophysics.
The main challenges of Inverse Problems are linked with such fundamental factors as non-linearity and ill-posedness of these problems. It is therefore natural that these challenges attract many mathematicians to work on both theoretical and computational aspects of this discipline. It is a hope of the Editorial Board that these two special issues would encourage mathematicians to submit good quality works in this journal.
Michael V. Klibanov
Victor Isakov
Masatiso Yamamoto
Guest Editors Footnote*
Notes
*Email addresses: [email protected], [email protected], [email protected]