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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:
 34G10 Linear differential equations in abstract spaces 47D03 Groups and semigroups of linear operators 35G10 Initial value problems for linear higher-order PDEs 35K25 Higher-order parabolic equations