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Zbl 0746.47023
Cioranescu, Ioana
On the second order Cauchy problem associated with a linear operator. (English)
[J] J. Math. Anal. Appl. 154, No.1, 238-242 (1991). ISSN 0022-247X

Let $A$ be a linear operator in a Banach space $X$ whose resolvent set contains $(0,\infty)$. The author defines a subspace $W$ of initial values $x\in X$ for which the second order abstract Cauchy problem $$u''(t)=Au(t), \qquad u(0)=x, \qquad u'(0)=0$$ has a solution on $\bbfR$. The space $W$ is contained in the Hille-Yosida subspace introduced by {\it S. Kantorovitz} [Math. Ann. 282, 535-544 (1988)].
[J.Voigt (Oldenburg)]

MSC 2000:: *47D09 Operator cosine functions and higher-order Cauchy problems

Keywords: operator cosine function; linear operator in a Banach space; resolvent; abstract Cauchy problem; Hille-Yosida subspace

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Zentralblatt MATH Berlin [Germany]