Library Building #502
National University of Mongolia
Invited Speakers
Ming Mei, McGill University & Champlain College
Mailasu, Inner Mongolia University
Sumiya Baasandorj, Scuola Normale Superiore
Registration 9:30–9:45
9:50–10:00
10:00–10:45
Ming Mei
McGill University & Champlain College
11:00–11:30
Baljinnyam Tsangia
Mongolian University of Science and Technology
11:30–12:00
Otgondorj Khuder
Mongolian University of Science and Technology
Lunch 12:00–14:00
14:00–14:40
Mailasu
Inner Mongolia University
15:00–15:30
Sumiya Baasandorj
Scuola Normale Superiore
15:40–16:10
Ariunaa Uuriintsetseg
Mongolian University of Science and Technology
Abstracts
Prof. Ming Mei
In this talk, we present our series of studies on Euler-Poisson equations with sonic boundary. Sonic boundary is a critical boundary, which with the doping profile causes many difficulties for the structure of solutions. We first study the structural stability of steady subsonic/ transonic solutions, when the doping profile is a small perturbation. Then, we study the quasi-neutral limits as the Debye length is vanishing. Finally we present the result on relaxation time limit. The singularity at the boundary layers makes the study to be challenging.
Prof. Mailasu
In this talk, we will consider the Newtonian limit of the free boundary value problem for the the cylindrical symmetric relativistic Euler equation and the spherically symmetric relativistic Euler-Poisson equation. Under the conditions of the free boundary and vacuum, we prove the existence and uniqueness of local smooth solutions of the relativistic Euler equation and the relativistic Euler-Poisson equation, which respectively converge to the solutions of the compressible Euler equation and the compressible Euler-Poisson equations at the rate of c^{-2}, where c is the speed of light. We also prove the relevant results on the local well-posedness of the compressible Euler (with damping) equation and the compressible Euler-Poisson equation.
Dr. Sumiya Baasandorj
In this talk, we discuss the stability of C1-alpha regularity for entropic optimal transport problems and its connection to Monge-Ampére equation. This is a recent joint work with Simone Di Marino and Augusto Gerolin.
Dr. Baljinnyam Tsangia
In 2009, Prof. Picard showed that a number of initial boundary-value problems of classical mathematical physics is generally represented in the linear operator equation and established the associated solution theory in a Hilbert space setting. We shall establish the solution theory of the evolutionary problems with a perturbation, which is defined by a quadratic form. As an example, we will consider the microwave heating problem.
Dr. Otgondorj Khuder
We propose four two-step derivative-free iterations of order 4 and 5 and twelve different three-step derivative-free iterations of order 6, 7 and 8. The main specific of these iterations is that they include vector or even scalar parameter of iteration instead of matrix parameter that inherent to other existing iterative methods. This factor make our algorithms computational efficient as compared to other known iterations. We made comparison of efficiency index of the proposed iterations. Theoretical conclusions of convergence order are confirmed by numerical examples.
Dr. Ariunaa Uuriintsetseg
We present Riemann solvers for a unified first-order hyperbolic formulation of continuum mechanics, capable of describing both fluids and solids simultaneously. Specifically, we have considered a generalization of the Osher Riemann solver and the HLLEM Riemann solver. Since the governing PDE system also contains non-conservative products, the use of path-conservative schemes becomes necessary to properly handle the non-conservative terms within the framework of weak solutions. The implementation and testing of the new Riemann solvers were successful, and these complete Riemann solvers clearly perform better than standard local Lax-Friedrichs-type or Rusanov-type Riemann solvers.