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

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ BV $\end{document}</tex-math></inline-formula>-solutions is obtained via vanishing viscosity in a suitable parameterized setting. In addition, we prove that the solution set is compact.