Title1: Some recent results on the Keller-Segel(-fluid) system
Speaker: Pro.Zhaoyin Xiang（University of Electronic Science and Technology of China）
Time: Mon, Apr.1, 2019, PM:15:00-16:00
Location: Room 4131, Building No.4, Wushan Campus
Abstract:
The software package BBCPOP is a MATLAB implementation of a hierarchy of sparse doubly nonnegative (DNN) relaxations of a class of polynomial optimization (minimization) problems (POPs) with binary, box and complementarity (BBC) constraints. Given a POP in the class and a relaxation order, BBCPOP constructs a simple conic optimization problem (COP), which serves as a DNN relaxation of the POP, and then solves the COP by applying the bisection and projection (BP) method. The COP is expressed with a linear objective function and constraints described as a single hyperplane and two cones, which are the Cartesian product of positive semidefinite cones and a polyhedral cone induced from the BBC constraints. BBCPOP aims to compute a tight lower bound for the optimal value of a large-scale POP in the class that is beyond the comfort zone of existing software packages. The robustness, reliability and efficiency of BBCPOP are demonstrated in comparison to the state-of-the-art software SDP package SDPNAL+ on randomly generated sparse POPs of degree 2 and 3 with up to a few thousands variables, and ones of degree from 5 to 8 with up to a few hundre
Title2: The small-convection limit in a chemotaxis-Navier-Stokes system
Speaker: Pro.Yulan Wang（Xihua University）
Time: Mon, Apr.1, 2019, PM:16:00-17:00
Location: Room 4131, Building No.4, Wushan Campus
Abstract:
In this talk, we consider an initial-boundary value problem for a chemotaxis-(Navier-)Stokes system in a bounded convex domain Ω ⊂R2 with smooth boundary. We concerns the limit problem in which the convection term in the Navier-Stokes system disappears and the Navier-Stokes part reduces to a forced evolutionary Stokes. The main result asserts temporally uniform convergence of solutions of the chemotaxis-Navier-Stokes system to the solution of its chemotaxis-Stokes counterpart.
