|Colloquium, 中正大學數學系 卓建宏教授|
Thursday, April 12, 16:10—17:00 數學系3174
Title: A Numerical Algorithm for Blow-up Problem
Abstract: In many evolution equations, solutions may become unbounded in finite time. This phenomenon is often called blow-up and the finite time is called the blow-up time. To numerically reproduce the finite-time blow-up phenomenon, schemes with adaptive time meshes were considered to be necessary. Since the numerical blow-up time is defined by an infinite sum, which implies that one needs to compute infinite times to achieve blow-up, this method cannot be carried out in real computation. As a consequence, we propose an algorithm accomplished by schemes with uniform time meshes for the computation of blow-up solutions. In this talk, we are concerned with a question: to what extent can this algorithm be applied to compute the blow-up solutions and reproduce the blow-up behavior?
|Colloquium, 臺灣大學數學系 陳俊全教授|
Thursday, April 19, 16:10—17:00 數學系3174
Title: Exact and Semi-Exact Solutions for the Lotka-Volterra 3-Species Competition System
Abstract: The phenomena in the Lotka-Volterra three-species competition-diffusion system are rich and complicated. In the joint work with Hung, Mimura, Tohma and Ueyama, we combined the method of exact/semi-exact solutions and the numerical approach to investigate the wave behaviors of this system. In this talk, we will explain our research and show that the exact/semi-exact solutions can provide very interesting information for the study of new dynamical patterns as well as the study of competitor-mediated coexistence in situations where one exotic competing species invades a system that already contains two strongly competing species. Also, some further applications of exact/semi-exact solutions will be discussed.
|PDE Seminar, Myongji University, Prof. Se Eun Noh|
Monday, April 23, 16:10—17:00 數學系3174
Title: Invariant Manifolds of the Steady Boltzmann Equation (2)
Abstract: NCKU-NCTS Reading Seminar on Kinetic Theory