Well-posedness of boundary value problems for a second-order equation
type: Item
instance of: scholarly article
title: Well-posedness of boundary value problems for a second-order equation
zbMATH Open document ID: 1205.34068
DOI: 10.1134/S1064562409050044
author: V. A. Kostin
author: M. N. Nebol'sina
published in: Doklady Mathematics
publication date: 2010-01-12T00:00:00Z
review text: Let \(E\) be a Banach space and let \(A\) be a positive operator acting on \(E\). The authors deduce an estimation for any weak solution of the equation \[ {d^2 u(t) \over d t^2} = A u(t), \quad 0 \leq t \leq T \leq \infty,\tag{1} \] if \(-A\) is the generator of an exponentially stable \(C_0\)-semigroup. Moreover, they establish conditions such that a weak solution is weakened. After that, the conclusions are extended to the study of the representation of bounded solutions for equation (1) and their weakened-type properties.
reviewed by: Bogdan Sasu
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 5656110
zbMATH Keywords: second-order equation
zbMATH Keywords: boundary value problem
MaRDI profile type: Publication
cites work: Q5332803
cites work: Q4040558
description: scientific article; zbMATH DE number 5656110