Lecturer: Qu Changzheng

Abstract:

It is well-known that the classical integrable systems adapt smooth solutions. Solutions reflect typical properties of integrable systems. It has been found that a number of integrable systems with nonlinear dispersion admit non-smooth solutions, which is regarded as an non- trivial feature of integrable systems. In this talk, we shall discuss stability of non-smooth solutions of integrable systems with nonlinear dispersion. First, we shall study the orbital stability of non-smooth peaked solutions of scalar equations. Second, orbital stability of non- smooth peaked solutions to systems is discussed. Finally, a Liouville property to an integrablesystem is investigated.

Introduction to the Lecturer:

Professor Qu Changzheng is a special-class expert of Zhejiang Province and a winner of the National Science Fund for Distinguished Young Scholars. He obtained his doctorate from the Department of Mathematics, Lanzhou University in 1993, successively did postdoctoral research in Northwest University and the Chinese University of Hong Kong, and made exchange visits in more than a dozen countries and regions such as the United States, Canada, Japan, Germany, Spain, Singapore and Hong Kong.

He is mainly engaged in the research on invariant geometric flow and its relationship with integrable system, as well as symmetry, invariants, geometric properties, solution singularity and stability of nonlinear partial differential equations. He has issued his main achievements in international famous journals such asComm. Math. Phys.,Adv. Math.,ARMA,Math. Ann.,J. Funct. Anal.,J. Math. Pure Appl.andNonlinearity. He has been invited to give a speech at some important academic conferences at home and abroad for many times. He is currently the editorial board member ofStud. Appl. Math.,Comm. Pure Appl. Anal.andAdvances in Mathematicsand the associate editor ofPure and Applied Mathematics. He was supported by key programs and general programs of the National Science Fund for Distinguished Young Scholars and the National Natural Science Foundation, and the Foundation of the Ministry of Education of China for Outstanding Young Teachers. His research achievements have won the first and second prizes of Scientific and Technological Progress of Shaanxi Province, the second prize of Natural Science Award of Zhejiang Province and the scientific and technological progress award of the State Education Commission.

Invitee:

Hu Xijun, Professor from School of Mathematics

Time:

15:30-16:20, November 25 (Thursday)

Venue:

Academic Hall #924, Block B, Zhixin Building, Central Campus

Hosted by School of Mathematics, Shandong University