Events for 10/26/2021 from all calendars

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: William Rundell, Texas A&M University

Title: Inverse problems for fractional and other nonlocal operators

Abstract: Fractional derivatives and powers of operators have been a well-studied topic over the last decade - and for good reason. Not only is there interesting mathematics involved but a myriad of applications from diverse areas of the physical sciences have shown that such operators in fact play a crucial role in correct modelling. In this talk we shall look at several inverse problems involving both classical derivatives and some of their fractional counterparts. The obvious question, which will come with some answers, is whether these two paradigms give similar uniqueness results. Many classical inverse problems for PDE are characterised by the fact that their solution is often highly ill-posed. This leads to the further question: are the ill-conditioning levels the same for both classical and fractional models? If not, can fractional operators be used as regularising approximations thus gaining intrinsic value even for classical derivatives?