CONTENTS Introduction 151 § 1. Maximal attractors of semigroups generated by evolution equations 156 § 2. Examples of parabolic equations and systems having a maximal attractor 158 § 3. The Hausdorff dimension of invariant sets 164 § 4. Estimate of the change in volume under the action of shift operators generated by linear evolution equations 167 § 5. An upper bound for the Hausdorff dimension...

We discuss `p-maximal regularity of power-bounded operators and relate the discrete to the continuous time problem for analytic semigroups. We give a complete characterization of operators with `1 and `∞-maximal regularity. We also introduce an unconditional form of Ritt’s condition for power-bounded operators, which plays the role of the existence of an H-calculus, and give a complete characte...

Abstract We consider the Dirichlet-to-Neumann operator associated to a strictly elliptic on space $$\mathrm {C}(\partial M)$$ C ( ∂ M ) of continuous functions boundary $$\partial M$$ compact manifold $$\overline{M}$$ <...

We address the problems of extrapolation, analyticity, and Lp-spectral independence for C0-semigroups in the abstract context of metric spaces with exponentially bounded volume. The main application of the abstract result is Lp-analyticity of angle π 2 of Schrödinger semigroups on Riemannian manifolds with Ricci curvature bounded below, under the condition of form smallness of the negative part...

In this paper the continuity of the solutions of a mathematical model of thermoviscoelasticity with respect to the model parameters is proved. This was an open problem conjectured iIi [27J and [28]. The nonlinear partial differential equations under consideration arise from the conservation laws of linear momentum and energy and describe structural phase transitions in solids with non-convex La...

We construct and study generalized Mehler semigroups (pt)t≥0 and their associated Markov processes M. The construction methods for (pt)t≥0 are based on some new purely functional analytic results implying, in particular, that any strongly continuous semigroup on a Hilbert space H can be extended to some larger Hilbert space E, with the embedding H ⊂ E being Hilbert-Schmidt. The same analytic ex...

In this note we relate two notions of compactness for strongly continuous semigroups of linear operators and cosine functions of linear operators. Specifically, if T denotes a strongly continuous semigroup of linear operators defined on a Banach space X, we will show that T is compact if and only if the set {(T(-)x : x £ X, \\x\\ < 1} is relatively compact in any space LP([Q, a]) ; X) for 1 < p...