Flow properties for Young-measure solutions of semilinear hyperbolic systems

We consider a semilinear hyperbolic system of d equations of first order.

We consider sequences of initial data which approximate a Young measure

and study the Young-measure limit of the associated sequence of solutions.

Thus we are able to define the notion of Cauchy problem and semigroups

for Young measure solutions, at least for by using compactness

through compensation. For the subclass of product measure solutions

is considered, where each Cauchy problem has a unique solution.

Continuous dependence of the associated semigroup on the initial

data can be established in the Wasserstein topology and, under additional

structural condition on the nonlinearity, also in the weak

ALIGN=TOP ALT="tex2html_wrap_inline12" SRC="/fileadmin/conf_img/conf44_am-img3.gif"> topology.

The reported research extends previous work of L. Tartar and

is partly joint work with Florian Theil.