On the convergence of hyperbolic semigroups in variable Hilbert spaces (Q997740)

Resolvent convergence is considered for nonnegative selfadjoint operators acting in variable Hilbert spaces \(H_{\varepsilon}\). The limit of the resolvents is, generally, a ``pseudoresolvent'' and not a resolvent. The situation may occur even for \(H_{\varepsilon}\equiv H\). This convergence is used for passing to the limit in the corresponding hyperbolic differential-operator equations in \(H_{\varepsilon}\) considered from the semigroup point of view. The scheme studied in the paper can be applied to the homogenization of nonstationary problems of elasticity for thin structures.