Perturbed sweeping process with a subsmooth set depending on the state (Q2821650)
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scientific article; zbMATH DE number 6629204
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Perturbed sweeping process with a subsmooth set depending on the state |
scientific article; zbMATH DE number 6629204 |
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22 September 2016
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differential inclusion
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sweeping process
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normal cone
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prox-regular set
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subsmooth set
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subdifferential
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Perturbed sweeping process with a subsmooth set depending on the state (English)
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The authors consider the perturbed sweeping process differential inclusions NEWLINE\[NEWLINE\begin{aligned} \dot u(t)&\in -N_{C(t,u(t))}(u(t))+G(t,u(t))\text{ a.e } t\in [0,T], \\ u(t)&\in C(t,u(t))\quad \forall t\in [0,T], \\ u(0)&=u_0\in C(0,u_0), \end{aligned}\tag{D} NEWLINE\]NEWLINE where \(C: [0,T]\times H\rightrightarrows H\) is a multimapping with nonempty closed values, \(H\) a Hilbert space, \(G: [0,T]\times H\rightrightarrows H\) is a multimapping with nonempty closed convex values and \(N_{C(t,u(t))}(\cdot)\) a normal cone to the set \(C(t,u(t)).\) Existence of solutions are proved when the sets \(C(t,u)\) are ball-compact and subsmooth.
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