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