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A characterization of energetic and $BV$ solutions to one-dimensional rate-independent systems

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  • The notion of BV solution to a rate-independent system was introduced in [8] to describe the vanishing viscosity limit (in the dissipation term) of doubly nonlinear evolution equations. Like energetic solutions [5] in the case of convex energies, BV solutions provide a careful description of rate-independent evolution driven by nonconvex energies, and in particular of the energetic behavior of the system at jumps.
        In this paper we study both notions in the one-dimensional setting and we obtain a full characterization of BV and energetic solutions for a broad family of energy functionals. In the case of monotone loadings we provide a simple and explicit characterization of such solutions, which allows for a direct comparison of the two concepts.
    Mathematics Subject Classification: Primary: 34C55, 47J20, 49J40; Secondary: 74N30.


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