Under suitable conditions we prove the wellposedness of small time-varied delay equations and then establish the robust stability for such systems on the phase space of continuous vector-valued functions.
We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter . Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.
Given a compact Hausdorff space and a strongly continuous semigroup of linear isometries of the Banach space of all complex-valued, continuous functions on , the semiflow induced by on is investigated. In the particular case in which is a compact, connected, differentiable manifold, a class of semigroups preserving the differentiable structure of is characterized.
Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral...
This is the second instalment of my previous paper with the same title, [1]. This paper consists of two different parts. The first part is devoted to improvements of the results developed in [1]. These improvements are described in section 0.1 below and developed in sections 1 to 5, and 9 to 10; they are in fact technically distinct from [1] and rely on a systematic use of microlocalisation in the context of Hörmander-Weyl calculus. These paragraphs can therefore be read quite independently from...
Soit un espace riemannien symétrique et l’espace des fonctions continues sur tendant vers 0 à l’infini. On démontre qu’un opérateur , invariant par les isométries de , engendre un semi-groupe fortement continu de contractions sur s’il est dissipatif et si son domaine contient les fonctions de classe à support compact.