Date: Friday, October 26, 2018
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: Fractional PDEs: control, applications, and beyond
Abstract: Fractional calculus and its application to anomalous transport has recently received a tremendous amount of attention. In these studies, the anomalous transport (of charge, tracers, fluid, etc.) is presumed attributable to longrange correlations of material properties within an inherently complex, and in some cases selfsimilar, conducting medium. Rather than considering an exquisitely discretized (and computationally explosive) representation of the medium, the complex and spatially correlated heterogeneity is represented through reformulation of the PDE governing the relevant transport physics such that its coefficients are, instead, smooth but paired with fractionalorder space derivatives.
This talk will give an introduction to fractional diffusion. We will describe how to incorporate nonhomogeneous boundary conditions in fractional PDEs. We will cover from linear to quasilinear fractional PDEs. New notions of optimal control and optimization under uncertainty will be presented. We will conclude the talk with an approach that allows the fractional exponent to be spatially dependent. This has enabled us to define novel Sobolev spaces and their trace spaces. Several applications in: imaging science, quantum random walks, geophysics, and manifold learning (data analysis) will be
discussed.
Files:
Speaker: Harbir Antil
Institution: George Mason University
Event Organizer: AIM seminar organizers
