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Solution semigroup and invariant manifolds for functional equations with infinite delay

Hana Petzeltová (1993)

Mathematica Bohemica

It is proved that parabolic equations with infinite delay generate $C_{0}$ -semigroup on the space of initial conditions, such that local stable and unstable manifolds can be constructed for a fully nonlinear problems with help of usual methods of the theory of parabolic equations.

Some applications of fractional calculus to operator semigroups and functional calculus

José E. Galé (2007)

Banach Center Publications

We survey some recent results on functional calculus for generators of holomorphic semigroups, which have been obtained using versions of fractional derivation of Riemann-Liouville or Weyl type. Such a calculus allows us to give tight estimates even in concrete L¹ examples.

Some condensation theorems for semigroup operators.

Oleg V. Davydov (1993)

Manuscripta mathematica

Some Landau's type inequalities for infinitesimal generators.

H. Kraljevic, J. Pecaric (1990)

Aequationes mathematicae

Some properties of weighted Sobolev spaces in $ℝ_{+}^{d}$

Nicolai V. Krylov (1999)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Some results on elliptic and parabolic equations in Hilbert spaces

Giuseppe Da Prato (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider elliptic and parabolic equations with infinitely many variables. We prove some results of existence, uniqueness and regularity of solutions.

Some spectral properties of the streaming operator with general boundary conditions

Mohamed Boulanouar (2008)

Applications of Mathematics

This paper deals with the spectral study of the streaming operator with general boundary conditions defined by means of a boundary operator $K$ . We study the positivity and the irreducibility of the generated semigroup proved in [M. Boulanouar, L’opérateur d’Advection: existence d’un $C_{0}$ -semi-groupe (I), Transp. Theory Stat. Phys. 31, 2002, 153–167], in the case $∥ K ∥ \geq 1$ . We also give some spectral properties of the streaming operator and we characterize the type of the generated semigroup in terms of the...

Spectral characterization of operators with precompact orbit

Andrzej Święch (1990)

Studia Mathematica

Spectral mapping theorem for integrated semigroups.

C.R. Day (1993)

Semigroup forum

Spectral projections, semigroups of operators, and the Laplace transform

Ralph deLaubenfels (1997)

Banach Center Publications

Square functions, bounded analytic semigroups, and applications

Christian Le Merdy (2007)

Banach Center Publications

To any bounded analytic semigroup on Hilbert space or on $L^{p}$ -space, one may associate natural ’square functions’. In this survey paper, we review old and recent results on these square functions, as well as some extensions to various classes of Banach spaces, including noncommutative $L^{p}$ -spaces, Banach lattices, and their subspaces. We give some applications to $H^{\infty}$ functional calculus, similarity problems, multiplier theory, and control theory.

Stability and ergodicity of dominated semigroups I. The uniform case.

Frank Räbiger (1993)

Mathematische Zeitschrift

Stability and ergodicity of dominated semigroups. II. The strong case.

Frank Räbiger (1993)

Mathematische Annalen

Stability and exactness

Marian Podhorodyński (1989)

Colloquium Mathematicae

Stability for non-autonomous linear evolution equations with $L^{p}$ -maximal regularity

Hafida Laasri, Omar El-Mennaoui (2013)

Czechoslovak Mathematical Journal

We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem $(P) \{\begin{matrix} \dot{u} (t) + A (t) u (t) = f (t) t -a.e. on [0, τ], u (0) = 0, \end{matrix}$ where $A : [0, τ] \to ℒ (X, D)$ is a bounded and strongly measurable function and $X$ , $D$ are Banach spaces such that $D \underset{d}{\to} ↪ X$ . Our main concern is to characterize $L^{p}$ -maximal regularity and to give an explicit approximation of the problem (P).

Stability of coupled systems.

Amar Khodja, Farid, Benabdallah, Assia, Teniou, Djamel (1996)

Abstract and Applied Analysis

Stability of strongly continuous representations of abelian semigroups.

Charles J.K. Batty, Vu Quoc Phóng (1992)

Mathematische Zeitschrift

Stabilizability and controllability of systems associated to linear skew-product semiflows.

Mihail Megan, Adina Luminita Sasu, Bogdan Sasu (2002)

Revista Matemática Complutense

This paper is concerned with systems with control whose state evolution is described by linear skew-product semiflows. The connection between uniform exponential stability of a linear skew-product semiflow and the stabilizability of the associated system is presented. The relationship between the concepts of exact controllability and complete stabilizability of general control systems is studied. Some results due to Clark, Latushkin, Montgomery-Smith, Randolph, Megan, Zabczyk and Przyluski are generalized....

Stabilizability in asymptotically finite-dimensional semigroups.

Storozhuk, K.V. (2003)

Sibirskij Matematicheskij Zhurnal

Stabilization of wave systems with input delay in the boundary control

Gen Qi Xu, Siu Pang Yung, Leong Kwan Li (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we consider a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight $(1 - μ)$ is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system generates a C0 group of linear operators. After a spectral analysis, we show that the closed loop system is a Riesz one, that is, there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis for the state Hilbert...

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