Direct and inverse scattering problems for the Schrodinger-type operators

Speaker: 赵越 副教授，华中师范大学

Inviter: 张海文

Title: Direct and inverse scattering problems for the Schrodinger-type operators

Language: Chinese

Time & Venue: 2025.12.17 15:00-16:00  #腾讯会议：482-795-794

Abstract: In this talk, we discuss direct and inverse scattering problems for the Schrodinger-type operators. For the direct problem, we investigate the meromorphic continuation of the resolvent of the classical Schrodinger operator with an unbounded potential. A logarithmic resonance-free region together with resolvent estimates in this region are derived. Relevant results on the fractional Schrodinger operator are also presented. For the inverse problem, we derive an increasing stability for the inverse potential scattering problem. By using multi-frequency data, the stability is obtained by establishing integral identities, resolvent estimates and analytic continuation. As a consequence, we do not use the construction of unphysical CGO solutions and thus the developed method can be used to deal with two-dimensional case. Further, the stability is extended to the magnetic Schrodinger equation for which the determination of both the magnetic and electric potentials is investigated. Our recent results on inverse random scattering problems will also be reported.