189767414
Zappa products
121961938
Bilateral semidirect products of transformation semigroups
17783663
Existence of Solutions for Degenerate Sweeping Processes
cf. e.g. [4], and also [11]. In this formulation, every E(x) ⊂ IR is a closed convex set (sometimes called the ”rigidity set”), t ≥ 0 denotes the process time, x ∈ Ω ⊂ IR is the material point, q ∈ IR an internal variable (like plastic strain or hardening), and W denotes a (modified) stored energy function. For our purpose of motivation, the main thing to note is that for every fixed x, the inclusion (2) is of type (1).
122068311
Yosida–Moreau Regularization of Sweeping Processes with Unbounded Variation
Lett↦C(t) be a Hausdorff-continuous multifunction with closed convex values in a Hilbert spaceHsuch thatC(t) has nonempty interior for allt. We show that the Yosida–Moreau regularizations of the sweeping process with moving setC(t), i.e., the solutions of[formula]are strongly pointwisely convergent asλ→0+to the solution of the corresponding sweeping process, formally written as[formula]