On a time and state dependent maximal monotone operator coupled with a sweeping process with perturbations
type: Item
instance of: scholarly article
title: On a time and state dependent maximal monotone operator coupled with a sweeping process with perturbations
zbMATH Open document ID: 1469.34057
author: Messaouda Benguessoum
author: Dalila Azzam-Laouir
author: C. Castaing
published in: Set-Valued and Variational Analysis
publication date: 2021-05-06T00:00:00Z
review text: In this paper, the authors consider the following couple of evolution inclusions governed by time and state dependent maximal operator and closed convex sweeping process, with perturbations of the form \[ \left\{\begin{aligned} -&\dot u(t)\in A(t,v(t))u(t)+f(t,u(t), v(t)) \quad && \text{a.e. } t\in [0,T],\\ &u(t)\in D(A(t,v(t)))&&\forall t\in [0,T],\\ -&\dot v(t)\in N_{C(t,u(t))}v(t)+g(t, u(t), v(t)) &&\text{a.e. } t\in [0,T],\\ &u(0)=u_0\in D(A(0,v_0)), &&v(0)=v_0\in C(0,u_0), \end{aligned}\right. \] where \(A(t,x)\) is a time and state dependent maximal monotone operator, \(D(A(t, x))\) stands for the domain of the operator \(A(t, x),\) \( C(t, x)\) is a time and state dependent closed convex set, \(N_{C(t,x)}\) is a sweeping process, and \(f , g\) are Carathéodory mappings. The existence of absolutely continuous solutions in separable Hilbert spaces is studied. Applications to optimization and Skorohod problems are also presented.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 28C20
zbMATH DE Number: 7345316
zbMATH Keywords: absolutely continuous
zbMATH Keywords: maximal monotone operator
zbMATH Keywords: pseudo-distance
zbMATH Keywords: sweeping process
MaRDI profile type: Publication
full work available at URL: s11228-020-00544-2
OpenAlex ID: W3030596986
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DOI: 10.1007/S11228-020-00544-2
description: scientific article; zbMATH DE number 7345316