Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads

We study a rate-independent system with non-convex energy in the case of a time-discontinuous loading. We prove existence of the rate-dependent viscous regularization by time-incremental problems, while the existence of the so called parameterized \begin{document}$ BV $\end{document} -solutions is obtained via vanishing viscosity in a suitable parameterized setting. In addition, we prove that the solution set is compact.