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Siberian Mathematical Journal

, Volume 46, Issue 2, pp 333–350 | Cite as

A generalization of the Hille-Yosida Theorem to the case of degenerate semigroups in locally convex spaces

  • V. E. Fedorov
Article

Abstract

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.

Keywords

semigroups of operators Sobolev-type equations locally convex spaces 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • V. E. Fedorov
    • 1
  1. 1.Chelyabinsk State UniversityChelyabinsk

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