Seminar meets Wednesdays at 2:00 pm in Parker 224 unless otherwise noted.
Special Applied and Computational Mathematics Seminar
Time and Day: Thursday March 22, 3:00--4:00
Place: Parker 320
Speakers: Feng Bao and Song Chen (each will give a 25min. presentation)
Title: An efficient algorithm for a nonlinear filtering problem
Abstract: We consider the classical filter problem where a signal process is modeled by a stochastic differential equation and the observation is perturbed by a white noise. The goal is to find the best estimation of the signal process based on the observation. Kalman Filter, Particle Filter, Zakai equations are some well known approaches to solve optimal filter problems. In this talk, we shall show the optimal filter problem can also be solved using forward backward doubly stochastic differential equations. Both theoretical results and numerical experiments will be presented.
Title: Poroelasticity: dilation dependent hydraulic conductivity
Abstract: The study of poromechanics is of great importance in our real life since lots of materials are considered to be porous, such as foam, soil, concrete, etc. In this talk we present a poroelasticity system with a dilation dependent hydraulic conductivity.
We first give a short introduction about poroelasticity and explain the classical Biot willis mode of consolidation. Then we obtain the well posedness of the quasi-static case coupling the momentum equation, which is elliptic and the diffusion equation, which is parabolic,. We prove the result using a modified Rothe's method for time discretization. After that we show the results for numerical solution of the PDE and prove the error estimate A numerical experiment is given in the end to demonstrate the convergence rate.
Speaker: Gary Sampson
Title: Two Weighted Estimates for Fourier Type Operators
Abstract: We prove two weighted estimates for Fourier transform type
operators. This includes the Fourier transform. We employ three articles
with W. B. Jurkat and one article with S. Bloom. "On maximal rearrangement
inequalities ..." Trans. AMS, (1984), "On rearrangement and weight
inequalities ..." Indiana U. Math. J., (1984), and "Two weighted (L^p,L^q)
estimates..." Rocky Mountain Math. J. (1993). We also obtain necessary and
sufficient conditions for weighted estimates for some sublinear operators.
Carleson's maximal operator is included here.
Speaker: Dmitry Glotov
Title: A Boundary Value Transformation for an Inverse Source Problem
Abstract: We consider a non-linear problem of determining the harmonic
function given the magnitude of its gradient on the boundary of a
domain. This problem originated in magnetometry as an inverse source
problem. The type of non-linearity considered here also arises in the
inverse conductivity problem with the interior data obtained from MRI
measurements. We present analysis for the two-dimensional case as well
as a reconstruction algorithm and some results of numerical experiments
both in 2d and 3d.
Speaker: Geraldo De Souza
Title: About the multiplication operator on Lorentz spaces
Abstract: In this talk, we use the new characterization of the Lorentz space
$L(p, 1)$ in order to characterize all functions $g$ so that the multiplication operator $M_g$ is bounded from the Lorentz space $L(p, r)$ into $L(p, r)$,
for $p, r > 1$.
Speaker: Bertram Zinner
Title: Creating online resources for mathematics
Abstract: Since last summer I have been working on creating online content for an introductory statistics course. In this talk I will discuss my experiences thus far, including the challenges posed by the process and the advantages of online teaching.
Thursday, November 18 3:30pm, Parker 250
Speaker: Farid Madani (Universitat Regensburg-Germany and NWF I-Mathematik Institute)
Title: Yamabe type equations
Abstract: Yamabe type equations are nonlinear PDEs defined on manifolds or on domains of R^n. In the last 40 years, they are intensively studied since they have applications in geometry. After introducing these equations, I will give some existence results of solutions and some applications in geometry.