BIMSA >
AMSS-YMSC-BIMSA Joint Seminar on Progress of Topology and Its Applications
Leibenson's equation on Riemannian manifolds
Leibenson's equation on Riemannian manifolds
Organizers
Haibao Duan
, Fei Han
, Yong Lin
, Jianzhong Pan
, Guo-Wei Wei
,
Jie Wu
, Kelin Xia
,
Shing Toung Yau
, Chao Zhou
Speaker
Alexander Grigor'yan
Time
Thursday, September 29, 2022 5:00 PM - 6:30 PM
Venue
1120
Online
Zoom 518 868 7656
(BIMSA)
Abstract
We consider on arbitrary Riemannian manifolds the Leibenson equation:
$$\partial _{t}u=\Delta _{p}u^{q}.$$
This equation comes from hydrodynamics where it describes filtration of a turbulent compressible liquid in porous medium. Here $u(x,t)$ is the fraction of the volume that the liquid takes in porous medium at time $t$ at point $x$. The parameter $p$ characterizes the turbulence of a flow, while $q$ describes the compressibility of the liquid.
We prove that if $p>2$ and $1/(p-1)
Speaker Intro
Professor Alexander Grigor'yan received his PhD from Lomonosov Moscow University in 1982. Since then, he worked at the State University of Volgograd and the Institute of Control Sciences in Moscow with receiving his habilitation in 1989. He has been a Humboldt Fellow at Bielefeld University in 1992-93 and a Guest Scholar at Harvard University in 1993/94. After working from lecturer to professor at Imperial College London in 1994-2005, he became a professor at Bielefeld University from 2005.
Professor Grigor'yan won a gold medal at International Mathematical Olympiad when he was 17, awarded by the Prize of the Moscow Mathematical Society in 1988, and received the Whitehead Prize of London Mathematical Society in 1997. He was an invited speaker of European Congress of Mathematicians in Barcelona in 2000.
Professor Grigor'yan is one of the top experts in geometric analysis on Riemannian manifolds, metric spaces and graphs, with making various important contributions on the topics.