Fedorov, V. E. A generalization of the Hille–Yosida theorem to the case of degenerate semigroups in locally convex spaces. (Russian, English) Zbl 1106.47035 Sib. Mat. Zh. 46, No. 2, 426-448 (2005); translation in Sib. Math. J. 46, No. 2, 333-350 (2005). Summary: The Hille–Yosida theorem about the infinitesimal generators of equicontinuous strongly continuous semigroups is generalized to the case of semigroups of Sobolev-type equations in locally convex spaces. The results take a rather simple form in semireflexive spaces. We study the phase spaces of Sobolev-type equations and apply the abstract results to a class of initial boundary value problems for nonclassical PDEs of high order which includes some problems of filtration theory. Cited in 10 Documents MSC: 47D06 One-parameter semigroups and linear evolution equations 34G10 Linear differential equations in abstract spaces 35M10 PDEs of mixed type 76S05 Flows in porous media; filtration; seepage Keywords:semigroups of operators; Sobolev-type equations; locally convex spaces PDF BibTeX XML Cite \textit{V. E. Fedorov}, Sib. Mat. Zh. 46, No. 2, 426--448 (2005; Zbl 1106.47035); translation in Sib. Math. J. 46, No. 2, 333--350 (2005) Full Text: EuDML EMIS OpenURL