Shenzhen University School of Mathematical Sciences  

Liyuan Scholars Colloquium Session 165

Title:  Darcy's law in Porous medium flows

Speaker: Professor Ronghua Pan (Georgia Institute of Technology)

Time: 14:30–16:00, April 29, 2026

Location: Room 3, Huixing Building, Yuehai Campus, Shenzhen University

Abstract:  The motion of Compressible flows in porous medium is naturally modeled by Compressible Euler equations with frictional damping. Although the system is hyperbolic, the large time behavior of solutions is conjectured to be governed by diffusive waves:  Darcy's law for momentum, and Porous Medium equation for density.  Even in one space dimension, the justification of this conjecture has been a longstanding open problem in Hyperbolic Conservation Laws. Another related important open problem is the global existence of BV solutions of the system with generic BV initial data. In this talk, I will survey the successful resolution of these problems. This talk is based on joint works with C. Dafermos, F. Huang, P. Marcati, and Z. Wang.

Speaker Profile:  Ronghua Pan is a professor at the Georgia Institute of Technology. He received his bachelor's degree in 1993 and his master's degree in 1995 from the University of Science and Technology of China, and his Ph.D. in mathematics from the Institute of Mathematics at the Chinese Academy of Sciences in 1998. He subsequently spent two years as a postdoctoral researcher at the Istituto Superiore di Scienze in Italy before joining the University of Michigan in 2000. He has been at Georgia Institute of Technology since 2003 and was appointed tenured full professor in 2011. Professor Pan Ronghua has produced a series of outstanding research results in the field of fluid dynamics equations and is one of the leading experts in this area.

All faculty and students are welcome!  

School of Mathematical Sciences  

April 27, 2026