Second order incomplete expiring Cauchy problems
type: Item
instance of: scholarly article
title: Second order incomplete expiring Cauchy problems
zbMATH Open document ID: 0683.47022
DOI: 10.1007/BF02573286
published in: Semigroup Forum
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134976
review text: On a Banach space let A be a linear operator with nonempty resolvent and consider the problem \[ u''(t)=A(u(t)),\quad u(0)=x,\quad \lim_{t\to \infty}\| u^{(k)}(t)\| =0,\quad k=0,1,2. \] This problem has a unique solution continuously depending on \(x\in {\mathcal D}(A)\) iff A has a square root that generates a \(C_ 0\) semigroup, that strongly converges to zero as t goes to infinity. Interesting applications to some partial differential equations close this well written paper.
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 4119037
zbMATH Keywords: second order Cauchy problem
zbMATH Keywords: square root
zbMATH Keywords: \(C_ 0\) semigroup
author: R. deLaubenfels
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4119037