Mini-symposium (MS)

MS6: Recent Developments on Partial Differential Equations and Applications

Organizers: Loc Nguyen, University of North Carolina at Charlotte

                     Dinh-Liem Nguyen, Kansas State University

Abstract: The area of Partial Differential Equations (PDEs) is an important research topic in both pure and applied mathematics. It is also an interdisciplinary area that involves Physics, Engineering, Biology, and many other fields. The goal of this mini-symposium is to bring together researchers working on different aspects of the field to discuss recent and new results in the field such as (1) the existence of unique or multiple solutions to PDEs, (2) regularity theory for PDEs, and (3) inverse problems for PDEs. Another goal of the mini-symposium is to promote idea exchange as well as potential future collaborations.

Saturday, September 18, 10:00 AM – 12:00 PM: Part I of III

Room: Libry 4129

10:00 – 10:30 Hung Tran, University of Wisconsin-Madison, Optimal rates of convergence in periodic homogenization of linear elliptic equations in non-divergence form

10:30 – 11:00 Luan Hoang, Texas Tech University, Infinite series asymptotic expansions for solutions of dissipative nonlinear differential equations

11:00 – 11:30 Dinh-Liem Nguyen, Kansas State University, Orthogonality sampling methods for inverse scattering problems

11:30 – 12:00 Khai Nguyen, North Carolina State University, A system of first order H-J equations related to an optimal debt management problem.

Saturday, September 18, 3:30 PM – 5:30 PM: Part II of III

Room: Libry 4129

3:30 – 4:00 Nam Le, Indiana University Bloomington, Convergence of an inverse iterative scheme for the Hessian eigenvalue

4:00 – 4:30 Thi-Phong Nguyen, Purdue University, Imaging scatterers from acoustic near-field measurements

4:30 – 5:00 Thu Le, Kansas State University, Sampling methods for bi-anisotropic Maxwell's equations

5:00 – 5:30 Loc Nguyen, University of North Carolina at Charlotte, Numerical viscosity solutions to Hamilton-Jacobi equations via a Carleman estimate and the convexification method

Sunday, September 19, 10:30 AM – 12:30 PM: Part III of III

Room: Libry 4129

10:30 – 11:00 Thuy Le, University of North Carolina at Charlotte, Convexification-based globally convergent numerical method for a 1D coefficient inverse problem with experimental data

11:00 – 11:30 Tuoc Phan, University of Tennessee-Knoxville, On well-posedness and regularity estimates of solutions to a class of degenerate parabolic equations

11:30 – 12:00 Trung Truong, Kansas State University, Inverse Born series method for a periodic inverse scattering problem

12:00 – 12:30 Khoa Vo, Florida A&M University, Convexification for a 3D inverse scattering problem with moving point sources