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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].

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