On the asymptotic behavior for a certain nonlinear evolution equation
type: Item
instance of: scholarly article
title: On the asymptotic behavior for a certain nonlinear evolution equation
zbMATH Open document ID: 0556.47033
DOI: 10.1016/0022-247X(84)90119-7
author: Kazuo Kobayasi
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: Let A be an accretive operator in a Banach space X which satisfies the range condition. Given \(x\in X\) and \(g:[0,\infty)\to [0,\infty)\) a nonincreasing continuous function such that g(t)\(\to 0\) as \(t\to \infty\), consider the initial value problem: \[ (E)\quad du(t)/dt+Au(t)+g(t)u(t)\ni g(t)x,\quad t\geq 0,\quad u(0)=x_ 0\in \overline{D(A)}. \] The asymptotic behavior of the (generalized) solution of (E) both at infinity and at the origin is studied by using the idea of Kohlberg and Neyman. Our results yield improvements of some results of Reich, Reich and Israel, and Miyadera. We also give a unified proof for these results.
Mathematics Subject Classification ID: 47H20
Mathematics Subject Classification ID: 47H06
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 3886618
zbMATH Keywords: accretive operator
zbMATH Keywords: range condition
zbMATH Keywords: initial value problem
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3886618