On a class of doubly nonlinear nonlocal evolution equations
type: Item
instance of: scholarly article
title: On a class of doubly nonlinear nonlocal evolution equations
zbMATH Open document ID: 1014.35051
author: Ulisse Stefanelli
published in: Differential and Integral Equations
publication date: 2003-07-08T00:00:00Z
review text: The abstract nonlinear evolution equation \(f\in (Au)' + Bu\) is investigated, where \(A\) is a (possibly degenerate) maximal monotone operator from a Hilbert space \(V\) to its dual \(V^*\), while \(B\) is a maximal monotone operator from \(L^2(0,T; V)\) to \(L^2(0,T;V^*)\) (\(T\) is a fixed positive number). Existence for this equation, with the Cauchy condition \(v_0\in Au(0)\), is proved by an approximation procedure. Applications to various integro-differential equations are also discussed. The paper includes a good description of the history of this topic. The main novelty here is the generality of the operator \(B\). In addition, the approximation procedure is a new approach to this kind of problems.
Mathematics Subject Classification ID: 35K90
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 35K85
Mathematics Subject Classification ID: 35R70
Mathematics Subject Classification ID: 47J35
zbMATH DE Number: 1839911
zbMATH Keywords: maximal monotone operator
zbMATH Keywords: integro-differential equations
reviewed by: Gheorghe Moroşanu
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1839911