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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.

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
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