Said Boulite

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The aim of this paper is to analyse a dynamic model which describes the spread of scrapie in a sheep flock. Scrapie is a transmissible spongiform encephalopathy, endemic in a few European regions and subject to strict control measures. The model takes into account various factors and processes, including seasonal breeding, horizontal and vertical(More)
We introduce polynomial stabilizability and detectability of well-posed systems in the sense that a feedback produces a polynomial stable C0–semigroup. Using these concepts, the polynomial stability of the given C0–semigroup governing the state equation can be characterized via polynomial bounds on the transfer function. We further give sufficient(More)
In this work, we use the extrapolation methods to study the existence and uniqueness of almost automorphic solutions to the semilinear boundary differential equation (SBDE) { x′(t) = Amx(t) + h(t, x(t)), t ∈ R, Lx(t) = g(t, x(t)), t ∈ R, where A := Am| kerL generates a hyperbolic C0-semigroup on a Banach space X and h, g are almost automorphic functions(More)
In this paper, admissibility of control operators for perturbed semigroups is considered. We prove that the set of admissible control operators for a semigroup generator is unchanged if we perturb this generator by an appropriate class of unbounded operators. The result is applied to prove the well-posedness of a class of time-delay systems.
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