Speaker : Barbara Kaltenbacher, University of Klagenfurt

Time : 15:00 - 16:00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

YouTube :  https://youtu.be/wvmIB_3mW3o

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Inverse problems, fractional PDE, coefficient identification, Newton’s method

Abstract:  We consider the inverse problem of recovering an unknown, spatially-dependent potential q(x) from a fractional order equation Lu+qu=f, defined in a two dimensional region of from boundary information. Here the differential operator L is a directionally fractional one, based on the Abel fractional integral. In the classical integer derivative case this reduces to recovering q in,

-Laplace u + q(x)u = f ,  which is a well-studied problem.

We develop both uniqueness and reconstruction results and show how the ill-conditioning of this inverse problem depends on the geometry of the region and the fractional orders used in x and y direction.

Biography: The main emphasis of my research lies in Inverse Problems and their regularization, where I have co-authored three monographs and contributed more than hundred journal papers. As this also involves modeling, analysis and numerics of the corresponding forward problems, I got involved in several application related topics such as piezoelectricty, hysteresis in magnetics and ferroelectrics, as well as nonlinear acoustics, where the latter has recently become another focus of my research with a monograph co-authorship and more than thirty journal papers so far.

My main achievements in regularization theory are on iterative regularization of nonlinear problems in Hilbert and also in general Banach spaces, as well as their efficient and stable implementation using and further developing modern techniques from numerics of PDEs and optimization. Concerning nonlinear acoustics, I have contributed to the analysis of classical and also advanced models.

This research has been supported by the Austrian and the German Science Foundations, as well as by industrial partners in a number of projects, that among others provided funding for the fifteen PhD students whom I had the pleasure to supervise so far.

Bibliography