A characterization of norm continuity of propagators for second order abstract differential equations

In this paper, we obtain a concise characterization of norm continuity for t > 0 of propagators for the complete second order abstract differential equation on a Banach space E, u″(t)+Bu′(t)+Au(t)=0, t≥0 where B ϵ L( E). As a consequence, we discover that a strongly continuous cosine operator fun...

Full description

Saved in:
Bibliographic Details
Published in:Computers & mathematics with applications (1987) 1998-07, Vol.36 (2), p.87-94
Main Authors: Liang, Jin, Xiao, Tijun
Format: Article
Language:English
Subjects:
Characterization
Norm continuity
Propagator
Second order abstract differential equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we obtain a concise characterization of norm continuity for t > 0 of propagators for the complete second order abstract differential equation on a Banach space E, u″(t)+Bu′(t)+Au(t)=0, t≥0 where B ϵ L( E). As a consequence, we discover that a strongly continuous cosine operator function or operator group is norm continuous for t > 0 if and only if its generator is bounded.
ISSN:0898-1221
1873-7668
DOI:10.1016/S0898-1221(98)00119-9