A characterization of energetic and \(BV\) solutions to one-dimensional rate-independent systems
The authors obtain a characterization of BV solutions and energetic solutions to rate-independent systems in the one-dimensional setting: \[ 0\in \partial \psi(u'(t)) + D \mathcal{E}_t(u(t)) \quad \text{in \(\mathbb{R}\), for a.e. \(t \in (0,T)\);} \] where \(\psi\) is a dissipation potential and the energy functional \(\mathcal{E}\) has the form \(\mathcal{E}_t(u) = W(u)-l(t)u\). Moreover, an explicit characterization of such solutions is given in the case when the loading \(l\) is monotone.
scientific article; zbMATH DE number 6144712