Distinguished Lecture Series
Friday, December 1, 2000
3:40-4:30, Room: PSF 123

Speaker:  Eitan Tadmor (UCLA)

Title:  Critical Threshold Phenomena in Euler-Poisson Equations

Abstract:

We study the solution of Euler-Poisson equations encountered in various
applications ranging from plasma physics to modeling of semi-conductors.
We show that if the initial configuration exceeds an intrinsic
critical threshold then the solution of these equations develop shock
discontinuities in a finite time, whereas initial configurations below
critical threshold lead to globally smooth solutions.  We also describe
the large time behavior of such solutions for various cases of charged
and uncharged particles, with or without viscosity and relaxation, in
one- and multi-dimensional configurations. It is shown that a critical
threshold phenomena, analogous to the break down of water waves on the
beach, is present in all these different cases.