Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).
Session Chair: Lauri Oksanen Session Chair: Teemu Kristian Tyni
Location:VG1.104
Presentations
Weakly nonlinear geometric optics and inverse problems for hyperbolic nonlinear PDEs
Plamen Stefanov
Purdue University, United States of America
We review recent results by the presenter, Antônio Sá Barreto, and Nikolas Eptaminitakis about inverse problems for the semilinear wave equation and the quasilinear Westervelt wave equation modeling nonlinear acoustic. We study them in a regime in which the solutions are not "small" so that we can linearize; when the nonlinear effects are strong and correspond to the observed phyisical effects. We show that a propagating high frequency pulse recovers the nonlinearity uniquely by recovering its X-ray transform, and we will show numerical simulations.
Identification of nonlinear effects in X-ray tomography
Yiran Wang
Emory University, United States of America
Due to beam-hardening effects, metal objects in X-ray CT often produce streaking artefacts which cause degradation in image reconstruction. It is known that the nature of the phenomena is nonlinear. An outstanding inverse problem is to identify the nonlinearity which is crucial for reduction of the artefacts. In this talk, we show how to use microlocal techniques to extract information of the nonlinearity from the artefacts. An interesting aspect of our analysis is to explore the connection of the artefacts and the geometry of metal objects.
Inverse problems for non-linear hyperbolic equations and many-to-one scattering relations
Matti Lassas
University of Helsinki, Finland
In the talk we give an overview on inverse problems for Lorentzian manifolds. We also discuss how inverse problems for partial differential equations can be solved using non-linear interaction of solutions. In the talk we concentrate on the geometric tools used to solve these problems, for instance to the k-to-1 scattering relation associated to the $k$-th order interactions and the observation time functions on Lorentzian manifolds.
Inverse problems for nonlinear elliptic PDE
Katya Krupchyk
University of California, Irvine, United States of America
We shall discuss some recent progress for inverse boundary problems for nonlinear elliptic PDE. Our focus will be on inverse problems for isotropic quasilinear conductivity equations, as well as nonlinear Schrodinger and magnetic Schrodinger equations. In particular, we shall see that the presence of a nonlinearity may actually help, allowing one to solve inverse problems in situations where the corresponding linear counterpart is open. This talk is based on joint works with Catalin Carstea, Ali Feizmohammadi, Yavar Kian, and Gunther Uhlmann.
