Shenzhen University School of Mathematical Sciences  

Liyuan Scholars Colloquium Session 155  

Title: The Boltzmann equation in an inffnite layer

Speaker: Professor Renjun Duan (The Chinese University of Hong Kong)  

Time: 16:00–17:00, December 10, 2025

Location: Shenzhen University Yuehai Campus International Conference Hall A

Abstract: We study the global-in-time dynamics of a rareffed gas ffow in a three-dimensional inffnite layer, governed by the nonlinear Boltzmann equation near global Maxwellians, supplemented with diffuse reffection boundary condition. It turns out that the solutions decay in time at a polynomial rate which is the same as that of solutions to the two-dimensional heat equation along the tangent direction. Furthermore, using spectral analysis we characterize the optimal large time asymptotic behavior of Boltzmann solutions toward diffusion wave solutions in an inffnite layer.

Speaker Profile:Duan Renjun, Professor at The Chinese University of Hong Kong. He received his Ph.D. in Science from City University of Hong Kong in 2008, followed by postdoctoral research at the Austrian Academy of Sciences. He has been a faculty member at The Chinese University of Hong Kong since 2010. He currently serves on the editorial boards of international journals including Nonlinear Analysis: Real World Applications, Discrete & Continuous Dynamical Systems (B), Kinetic and Related Models, and Communications in Mathematical Analysis and Applications. His long-term research focuses on the mathematical study of nonlinear partial differential equations, with significant achievements in the Boltzmann equation and dissipative partial differential equations. In 2024, he received funding from the National Natural Science Foundation of China's Outstanding Young Scientist Fund.

All faculty and students are welcome!  

School of Mathematical Sciences  

December 4, 2025