BV solutions of nonconvex sweeping process differential inclusion with perturbation

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Existence and Uniqueness of Solutions for Non-Autonomous Complementarity Dynamical Systems (2010, methodology): “According to [15] a mapping z : [0,+∞[→ R is a solution of (15) with z0 as initial condition if: (i) z(·) is locally rcbv and satisfies z(0) = z0 and z(t) ∈ S(t) for all t ∈ [0,+∞[; (ii) there exists a positive Radon measure ν absolutely continuously equivalent to the measure μ + λ and with respect ”
Discontinuous sweeping process with prox-regular sets (2017, methodology): “Following [1, 12], we define the concept of solution for our measure differential inclusion as follows: Definition 4.”
A MACROSCOPIC CROWD MOTION MODEL OF GRADIENT FLOW TYPE (2010, methodology): “In the first case, Cauchy-Lipschitz theory for ODE’s applies, whereas CD models present some analogies with the so-called sweeping process introduced by Moreau[36] in the 70’, for which a dedicated framework has been developped (see [20], [21], [35]).”
A mathematical framework for a crowd motion model (2008, methodology): “Néanmoins, le caractère proxrégulier de Q (voir [4]) permet d’assurer le caractère bien posé du problème, grâce à des résultats récents de [3,4] sur le processus de rafle (voir Théorème 2.”
Prox-regular sets and epigraphs in uniformly convex Banach spaces: Various regularities and other properties (2011, background): “, [19, 24, 42]), in resource allocation mechanisms in economics (see, e.”