Non-convex perturbation to evolution problems involving Moreau’s sweeping process. (English) Zbl 07801511
Summary: Along this paper, we study an evolution inclusion governed by the so-called sweeping process. The right side of the inclusion contains a set-valued perturbation, supposed to be the external forces exercised on the system. We prove existence and relaxation results under weak assumptions on the perturbation by taking a truncated Lipschitz condition. These perturbations have non-convex and unbounded values without any compactness condition; we just assume a linear growth assumption on the element of minimal norm. The approach is based on the construction of approximate solutions. The relaxation is obtained by proving the density of the solution set of the original problem in a closure of the solution set of the relaxed one.
MSC:
| 47L07 | Convex sets and cones of operators |
| 47J35 | Nonlinear evolution equations |
| 28B20 | Set-valued set functions and measures; integration of set-valued functions; measurable selections |
| 49J52 | Nonsmooth analysis |
| 46N10 | Applications of functional analysis in optimization, convex analysis, mathematical programming, economics |
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