Nonlocal quasivariational evolution problems
type: Item
instance of: scholarly article
title: Nonlocal quasivariational evolution problems
zbMATH Open document ID: 1114.34044
author: Ulisse Stefanelli
published in: Journal of Differential Equations
publication date: 2006-12-07T00:00:00Z
review text: This is a valuable paper indeed. The existence of the evolution problem \[ u'(t)+\partial\varphi(u,t,u(t))\ni 0 \] with \(u(0)=u_0\) in a Hilbert space \(H\) is studied. We emphasize the functional dependence of \(\varphi\) on \(u\) in order to take into account nonlocal in time effects. The function \(\varphi\) is convex in its last variable and \(\partial\) stands for the subgradient with respect to it. The existence of weak solutions relies on an order structure and on a fixed point theorem for multivalued maps on ordered sets. Various examples are included: Moreau's sweeping process, quasivariational sweeping process, gradient flow, parabolic variational inequalities, parabolic evolution problems.
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 47J20
zbMATH DE Number: 5078199
zbMATH Keywords: quasivariational inequalities
zbMATH Keywords: order techniques
zbMATH Keywords: fixed point
zbMATH Keywords: nonlocality
reviewed by: Ovidiu Cârjă
MaRDI profile type: Publication
full work available at URL: j.jde.2006.05.004
OpenAlex ID: W2055328236
cites work: Q5186236
cites work: Numerical analysis of a three‐dimensional super‐elastic constitutive model
cites work: WELL-POSEDNESS AND APPROXIMATION FOR A ONE-DIMENSIONAL MODEL FOR SHAPE MEMORY ALLOYS
cites work: Q3344749
cites work: Q4094029
cites work: Q5680673
cites work: Q5665783
cites work: Sur la régularité de la solution d'inéquations elliptiques
cites work: Q4669347
cites work: Nonlinear evolution equations in Banach lattices
cites work: Nonlinear equations of evolution
cites work: On T-accretive operators
cites work: Opérateurs accrétifs et \(\varphi\)-accrétifs dans un espace de Banach
cites work: Q4097611
cites work: Plasticity. Mathematical theory and numerical analysis
cites work: Q3998992
cites work: The gradient of a convex function on a regular functional space and its potential theoretic properties
cites work: Potential theoretic properties of the gradient of a convex function on a functional space
cites work: On Completeness of Partially Ordered Sets and Fixpoint Theorems for Isotone Mappings
cites work: On parabolic quasi-variational inequalities and state-dependent sweeping processes
cites work: Q2765778
cites work: A uniqueness theorem for elliptic quasi-variational inequalities
cites work: Differential inclusions in nonsmooth mechanical problems. Shocks and dry friction
cites work: Q4061377
cites work: Inéquations d'évolution paraboliques avec convexes dependant du temps. Applications aux inéquations quasi-variationnelles d'évolution
cites work: Q3845569
cites work: Q5657753
cites work: Q5662351
cites work: Evolution problem associated with a moving convex set in Hilbert space
cites work: Q5662971
cites work: Q4366537
cites work: An order approach to a class of quasivariational sweeping processes
cites work: On a class of doubly nonlinear nonlocal evolution equations
cites work: On some nonlocal evolution equations in Banach spaces
cites work: Q3594110
cites work: Q4101037
DOI: 10.1016/J.JDE.2006.05.004
description: scientific article; zbMATH DE number 5078199