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

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.