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A characterization of norm continuity of propagators for second order abstract differential equations. (English) Zbl 0932.34064
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 $$E$$, $u''(t)+ Bu'(t)+ Au(t)= 0,\quad t\geq 0,$ 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:
 34G20 Nonlinear differential equations in abstract spaces
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##### References:
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