ΕΚΔΗΛΩΣΕΙΣ

ΣΕΜΙΝΑΡΙΟ ΕΦΑΡΜΟΣΜΕΝΗΣ ΑΝΑΛΥΣΗΣ & ΜΔΕ: INVERSE SCATTERING FOR QUASILINEAR OPERATORS OF HIGHER ORDER

Παρασκευή 18 Ιουνίου 2021
Σεμινάριο Εφαρμοσμένης Ανάλυσης & ΜΔΕ: Inverse scattering for quasilinear operators of higher order

Σύνδεσμος: meet.google.com/sru-gxoc-gzw

Ημερομηνία: Παρασκευή 18/6/2021

Ώρα: 15:15

Ομιλητής: Valery Serov (University of Oulu, Finland)

Τίτλος: Inverse scattering for quasilinear operators of higher order

Περίληψη: The subject of this work concerns the classical direct and inverse scattering problems for quasi-linear perturbations of the multidimensional biharmonic operator. The quasi-linear perturbations of the first and zero order might be complex-valued and singular. We show the existence of the scattering solutions to the direct scattering problem in the Sobolev space. Then the inverse scattering problem can be formulated as follows: does the knowledge of the far field pattern uniquely determine the unknown coefficients for given differential operator? It turns out that the answer to this classical question is affirmative for quasi-linear perturbations of the biharmonic operator also. Moreover, in the absence of the
uniqueness theorem, we present an approximate method (inverse backscattering Born approximation) for the reconstruction of the singularities of unknown coefficients.