报告题目：Efficient numerical methods for Helmholtz optimal cont…

报 告 人：张凯

时 间：2019年9月27日 下午 2：30-3：30

地 点：六号楼二楼报告厅

简 介：Efficient numerical methods for solving Poisson equation constraint optimal control problems with random coefficient are discussed in this talk. By applying the finite element method and the Monte Carlo approximation, the original optimal control problem is discretized and transformed into an optimization problem. Taking advantage of the separable structures, Algorithm 1 is proposed for solving the problem, where an alternating direction method is used. Both computational and storage costs of this algorithm are very high. In order to reduce the computational cost, Algorithm 2 is proposed, where the multi-modes expansion is introduced and applied. Further, in order to reduce the storage cost, we propose Algorithm 3 based on Algorithm 2. The main idea is that the random term is shifted to the objective functional, which could be computed in advance. Therefore, we only need to solve a deterministic optimization problem, which could reduce all the costs significantly. Moreover, the conv...

报告题目：Bifurcations of Travelling Wave Solutions for Fully No…

报 告 人：李继彬

时 间：2019年9月19日（周四）上 午 8:30-9:30

地 点：六号楼二楼报告厅

简 介：For the generalized Serre-Green-Naghdi equations with surface tension, by using the methodologies of dynamical systems and singular traveling wave theory developed Li & Chen [2007] to their travelling wave systems, in different parameter conditions of the parameter space, all possible bounded solutions (solitary wave solutions, kink wave solutions, peakons, pseudo-peakons and periodic peakons as well as compactons) are obtained. More than 26 explicit exact parametric representations are given. It is interesting to find that this fully nonlinear water waves equation has coexistence of uncountably infinitely many smooth solitary wave solutions or uncountably infinitely many pseudo-peakon solutions with periodic solutions or compacton solutions. Differing from the well-known peakon solution of the Camassa-Holm equation, the generalized Serre-Green-Naghdi equations have four new forms of peakon solutions.

报告题目：Limit cycle bifurcations of piecewise smooth near-Hami…

报 告 人：韩茂安

时 间：2019年9月19日（周四）上 午 9:30-10:30

地 点：六号楼二楼会议室

简 介：This paper deals with the number of limit cycles for planar piecewise smooth near-Hamiltoian or near-integrable systems with a switching curve. The main task is to establish a so-called first order Melnikov function which plays a crucial role in the study of the number of limit cycles bifurcated from a periodic annulus. We use the function to study Hopf bifurcation when the periodic annulus has an elementary center as its boundary. As applications, using the first order Melnikov function, we consider the number of limit cycles bifurcated from the periodic annulus of a linear center under piecewise linear polynomial perturbations with three kinds of quadratic switching curves. And we obtain 3 limit cycles for each case.