Series: Mathematics Colloquium

Date: Thursday, November 14, 2002

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Yuxi Zheng

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: Alberto Bressan, SISSA, Trieste

Title: One Dimensional Hyperbolic Systems of Conservation Laws

Abstract:

The talk will survey recent progress in the theory of nonlinear
hyperbolic systems in one space dimension.  In particular, I shall
first review the main results on uniqueness and continuous dependence
of entropy weak solutions, together with error estimates.  The main
focus will be on the uniform BV bounds, stability and convergence of
vanishing viscosity approximations, recently proved by S. Bianchini
and the speaker.  These results are obtained by a decomposition of the
solution as a sum of travelling wave profiles, and the introduction of
new Lyopunov functionals, controlling various types of viscous wave
interactions.