Invited by Prof. Chunyou Sun of School of Mathematics and Statistics,

Prof. Xiaoming Wang of Southern University of Science and Technology will visit our school and give a lecture during his staying from June 30th to July 6th in 2019.

Title: Approximating long-time statistical properties of infinite dimensional dissipative dynamical systems

Time：9: 00 am, July 3rd, 2019

Location：Lecture Room, Mingdao Building, Medical Compus of Lanzhou Univerisity

Abstract: It is well-known that physical laws for large chaotic dynamical systems are evealed statistically. The main concern of this talk is numerical methods for issipative chaotic infinite dimensional dynamical systems that are able to capture the stationary statistical properties of the underlying dynamical systems. We first survey results on temporal and spatial approximations that enjoy the desired properties. We then present a new result on fully discretized approximations of infinite dimensional dissipative chaotic dynamical systems that are able to capture asymptotically the stationary statistical properties. The main ingredients in ensuring the convergence of the long time statistical properties of the numerical schemes are: (1) uniform dissipativity of the scheme in the sense that the union of the global attractors of the numerical approximations is pre-compact in the phase space; (2) convergence of the solutions of the numerical scheme to the solution of the continuous system on the unit time interval [0, 1] modulo an initial layer, uniformly with respect to initial data from the union of the global attractors. The two conditions are reminiscent of the Lax equivalence theorem where stability and consistency are needed for the convergence of a numerical scheme.

Curriculum Vitae:Professor Wang Xiaoming graduated from Fudan University and received his Ph.D. from Indiana University in Bloomington in 1996. In the following two years, he worked as a postdoctoral researcher at the famous Coulometric Institute of New York University (Culang Lecturer); in 1998, he joined the Department of Mathematics at Iowa State University. In 2001, he was promoted to associate professor and tenured. In 2002, he worked in Cullen. The Institute and the Princeton Institute of Advanced Studies acted as researchers; in 2003, he was invited to join Florida State University as a tenured professor and was promoted to full professor in 2006. During his tenure at Florida State University, he served as Director of Applied and Computational Mathematics (2009-2012) and Head of the Department of Mathematics (2012-2017). In 2017, he was invited to join his alma mater, Fudan University, as a special professor; in 2018, he joined Southern University of Science and Technology and is currently the head of the Department of Mathematics and professor.

Provincial Key Laboratory of Applied Mathematics and Complex Systems, Gansu Province

School of mathematics and statistics

CuiyingHonors College

July 1st, 2019