Doubly nonlinear equations with unbounded operators
type: Item
instance of: scholarly article
title: Doubly nonlinear equations with unbounded operators
zbMATH Open document ID: 1073.34076
author: Veli-Matti Hokkanen
author: Sergiu Aizicovici
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-10-12T00:00:00Z
review text: The authors investigate the following nonlinear evolution system \[ \begin{align*}{& v'(t)+w(t)=\tilde{f}(t)\quad\text{for a.a. } t\in ]0,T[,\cr & v(t)\in {\cal A}(t)u(t),\quad w(t)\in {\cal B}(t)u(t)\quad\text{for a.a. } t\in ]0,T[,\cr & v(0)=v_0,}\end{align*} \] where the operators \({\mathcal A}(t)\) and \({\mathcal B}(t)\) are subdifferentials of proper convex lower semicontinuous functions on a real Hilbert space \(V\) such that \({\mathcal A}(t)+{\mathcal B}(t)\) is \(V\)-coercive. They consider the case, when \({\mathcal A}(t)\) are bounded and possibly degenerate subdifferentials and \({\mathcal B}(t)\) are unbounded subdifferentials. The authors formulate conditions which guarantee the existence of solutions of the above system if the initial value \(v_0\) belongs to the range of \({\mathcal A}(0)\) and \(\tilde{f}\) is differentiable. As an example a variational inequality is considered.
reviewed by: Dariusz Bugajewski
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 47J35
zbMATH DE Number: 2107300
zbMATH Keywords: nonlinear evolution system
zbMATH Keywords: maximal monotone operator
MaRDI profile type: Publication
full work available at URL: j.na.2003.10.029
OpenAlex ID: W1972475980
Wikidata QID: Q110035344
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DOI: 10.1016/J.NA.2003.10.029
description: scientific article; zbMATH DE number 2107300