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On $K(t)$-convoluted semigroups. (English) Zbl 0828.34046
McBride, A. C. (ed.) et al., Recent developments in evolution equations. Proceedings of a meeting held at the University of Strathclyde, UK, 25-29 July, 1994. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 324, 86-93 (1995).
Summary: For problems of the type $u'= Au$, $u(0)= x$, in a Banach space $X$, we consider the regularized problems $v'= Av+ K(t)x$, $v(0)= 0$ ($K$ being a scalar kernel) and study the evolution operators $S_K(t)$ giving the (local mild) solutions; we obtain generation results generalizing and improving earlier Hille-Yosida type results and give an application to multiplication operators in $L^p$-spaces. For the entire collection see [Zbl 0817.00013].

MSC:
34G10Linear ODE in abstract spaces
47D03(Semi)groups of linear operators
35G10Initial value problems for linear higher-order PDE
35K25Higher order parabolic equations, general