Asymptotic behavior of bounded solutions to some second order evolution systems
type: Item
instance of: scholarly article
title: Asymptotic behavior of bounded solutions to some second order evolution systems
zbMATH Open document ID: 1216.47108
DOI: 10.1216/RMJ-2010-40-4-1289
author: Behzad Djafari Rouhani
author: H. Khatibzadeh
published in: Rocky Mountain Journal of Mathematics
publication date: 2010-09-07T00:00:00Z
review text: From the abstract: By using previous results of Rouhani for dissipative systems, we study the asymptotic behavior of solutions to the following second order evolution equation \[ u''(t)-cu'(t)\in Au(t),\qquad u(0)=u_0, \qquad \sup_{t\geq 0} |u(t)|<+\infty , \] where \(A\) is a maximal monotone operator in a real Hilbert space \(H\) and \(c\geq 0\). We investigate weak and strong convergence theorems for solutions to this system. Our results extend and unify previous results by Mitidieri and by Morosanu who studied the case \(c=0\) by assuming that \(A\) is maximal monotone and \(A^{-1}(0)\not= \emptyset\), as well as previous results by Veron who studied the case \(c>0\) by assuming \(A\) to be strongly monotone.
Mathematics Subject Classification ID: 47J35
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 47H05
zbMATH DE Number: 5779829
zbMATH Keywords: second order evolution equation
zbMATH Keywords: monotone operator
zbMATH Keywords: asymptotic behaviour
zbMATH Keywords: nonexpansive curve
zbMATH Keywords: ergodic theorem
zbMATH Keywords: weak convergence
reviewed by: Nguyen Van Minh
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5779829