Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads. (English) Zbl 1458.35439

Summary: 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 BV-solutions is obtained via vanishing viscosity in a suitable parameterized setting. In addition, we prove that the solution set is compact.


35R05 PDEs with low regular coefficients and/or low regular data
49J40 Variational inequalities
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
35Q74 PDEs in connection with mechanics of deformable solids
35D40 Viscosity solutions to PDEs
49J45 Methods involving semicontinuity and convergence; relaxation
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