Strong Traces for Conservation Laws with General Nonautonomous Flux

Source abstract

This paper concerns the trace problem for quasi-solutions of scalar conservation laws defined in $\Omega \subset {\mathbb R}^{n+1}$ with roughly nonautonomous flux functions $f \in L^1_\text{loc}(\Omega;C({\mathbb R})^{n+1})$. Under a nondegeneracy condition of $f$ at the boundary of $\Omega$, we show a strong trace on it.