## EVENT DETAILS AND ABSTRACT

**PDE Seminar**
**Title:** On the structure of solutions of multidimensional systems of conservation laws

**Speaker:** Professor Monica Torres

**Speaker Info:** Purdue University

**Brief Description:**

**Special Note**:

**Abstract:**

We obtain strong traces of
solutions of multidimensional systems of conservation laws assuming
a weaker regularity property on
the entropy solution $u \in L^\infty(R^{d+1},R^m)$. More precisely, given any
entropy function $\eta$ and any hyperplane
$ \{(t,x): x \in R^d\}$, we show that if
$u \in L^\infty(R^{d+1},R^m)$ is an entropy solution that
satisfies the vanishing mean oscillation
property on half balls, then
$\eta(u)$ has strong traces
$H^d$-almost everywhere on the hyperplane. For the general case, given any
set of finite perimeter $E$ and $
nu: \delta^*E \to \mathbb{S}^d$ its inner unit
normal and assuming the vanishing mean oscillation property on half
balls, we show that the weak trace of the vector field
$(\eta(u), q(u))$ is indeed strong, for any entropy
pair $(\eta, q)$.

**Date:** Thursday, June 05, 2008

**Time:** 4:10pm

**Where:** Lunt 105

**Contact Person:** Prof. Gui-Qiang Chen

**Contact email:** gqchen@math.northwestern.edu

**Contact Phone:** 847-491-5553

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Department of Mathematics, Northwestern University.