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

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Abstract

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.

Keywords

Characterization
Norm continuity
Propagator
Second order abstract differential equation

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This work was supported by the National NSF of China and the ABSF of Yunnan Province.