Mini-symposium (MS) 

MS16: Recent Advances in Nonlinear Wave Propagation and Interaction

Organizers: Ilija Jegdic, Texas Southern University

                     Qi Han, Texas A&M University San Antonio

Abstract: The nonlinear wave phenomenon appears in a wide range of applications in sciences and engineering, including fluid dynamics, elastodynamics, electromagnetic, and other fields. The study of partial differential equations modeling nonlinear wave propagation and interaction involves an interplay between the pure mathematical theory, numerical methods, and mathematical physics. An interesting feature of these equations is that solutions could become irregular even for smooth initial and boundary data and one of the challenges in the study of such solutions is to select physically meaningful solutions.

Recently, there has been lot of progress in the study of these equations and the purpose of this mini-symposium is to bring together mathematicians working on various problems both from theoretical and numerical perspectives. Some of the topics to be discussed include analysis of solutions to eikonal-type equations; study of existence, uniqueness, and stability of subsonic flows past an airfoil governed by the Euler gas dynamics equations; analysis of solutions to the two-layer quasigeotropic model; as well as convergence analysis of a large time step numerical method for conservation laws and numerical schemes for modified Buckley-Leverett equations and the black oil problem in porous media.

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

Room: Libry 3133

10:00 – 10:30 Loic Cappanera, University of Houston, Discontinuous Galerkin method for black oil problem: convergence and analysis

10:30 – 11:00 Ying Wang, University of Oklahoma, Mathematical analysis and numerical studies for the modified Buckley-Leverett equations

11:00 – 11:30 Jun Chen,Yichun College, Jiangxi, China, Stability of voertex lines attached to a thin airfoil

11:30 – 12:00 Elefterios Gkioulekas, University of Texas at Rio Grande Valley, The effect of the asymmetric Ekman term on the phenomenology of the two-layer quasigeostropic model

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

Room: Libry 3133

3:30 – 4:00 Katarina Jegdic, University of Houston, Semi-hyperbolic patches for the unsteady transonic small disturbance equation

4:00 – 4:30 Evan Milliken, University of Louisville, Bistability in determistic and stochastic SLIAR-type models with impercet and waning vaccine protection

4:30 – 5:00 Jing Tian, Towson University, Study of chaotic vibration phenomeon of the non-strictly hyperbolic equation

5:00 – 5:30 Zhaosheng Feng, University of Texas at Rio Grande Valle, Wave solutions to KdV-Burgers-type systems

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

Room: Libry 3133

10:30 – 11:00 George Avalos, University of Nebraska Lincoln, Stability analysis of interactive fluid and multilayered structure PDE dyamics

11:00 – 11:30 Pelin Guven Geredeli, Iowa State University, Properties of a coupled compressible flow-plate dynamics

11:30 – 12:00 Yue Chen, Auburn University Montgomery, Controlling refraction using sub-wavelength resonators

12:00 – 12:30 Wen Feng, Niagara University, Large-time behavior of 2D incompressible MHD system with partial dissipation