It is proved that parabolic equations with infinite delay generate -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.
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.
We consider elliptic and parabolic equations with infinitely many variables. We prove some results of existence, uniqueness and regularity of solutions.
This paper deals with the spectral study of the streaming operator with general boundary conditions defined by means of a boundary operator . We study the positivity and the irreducibility of the generated semigroup proved in [M. Boulanouar, L’opérateur d’Advection: existence d’un -semi-groupe (I), Transp. Theory Stat. Phys. 31, 2002, 153–167], in the case . We also give some spectral properties of the streaming operator and we characterize the type of the generated semigroup in terms of the...
To any bounded analytic semigroup on Hilbert space or on -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 -spaces, Banach lattices, and their subspaces. We give some applications to functional calculus, similarity problems, multiplier theory, and control theory.
We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem where is a bounded and strongly measurable function and , are Banach spaces such that . Our main concern is to characterize -maximal regularity and to give an explicit approximation of the problem (P).
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....
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 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...