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Zbl 0932.34064
Liang, Jin; Xiao, Tijun
A characterization of norm continuity of propagators for second order abstract differential equations.
(English)
[J] Comput. Math. Appl. 36, No.2, 87-94 (1998). ISSN 0898-1221

Summary: The authors obtain a concise characterization of the norm continuity for $t>0$ of propagators for the complete second-order abstract differential equation on a Banach space $E$, $$u''(t)+ Bu'(t)+ Au(t)= 0,\quad t\ge 0,$$ with $B\in L(E)$. As a consequence, they 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.
MSC 2000:
*34G20 Nonlinear ODE in abstract spaces

Keywords: norm continuity; propagators; complete second-order abstract differential equation; operator group

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