Lipschitz approximation of the sweeping (or Moreau) process
The sweeping process introduced by Moreau can be described as follows. Let C(0) be some closed convex set which moves in a Euclidean, or Hilbert space. C(t) describes the position of this set at time t, \(t\geq 0\). A point in C(0) does not move until such time \(\bar t\) when the boundary of \(C(\bar t)\) touches it. Then it is a boundary point of \(C(\tau)\) for all \(\tau\geq \bar t\) (as the boundary pushes it). Moreau showed that some problems in elastoplasticity can be described in terms of such sweeping processes. The author offers a proof of existence and uniqueness of a sweeping process with a given initial condition, and makes some improvements in related results of Moreau and Monteiro Marques.
scientific article; zbMATH DE number 4179846
scientific article