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Second order evolution equations with parameter

Jan Bochenek, Teresa Winiarska (1994)

Annales Polonici Mathematici

We give some theorems on continuity and differentiability with respect to (h,t) of the solution of a second order evolution problem with parameter h Ω m . Our main tool is the theory of strongly continuous cosine families of linear operators in Banach spaces.

Semiflows and semigroups

Edoardo Vesentini (1996)

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

Given a compact Hausdorff space K and a strongly continuous semigroup T of linear isometries of the Banach space of all complex-valued, continuous functions on K , the semiflow induced by T on K is investigated. In the particular case in which K is a compact, connected, differentiable manifold, a class of semigroups T preserving the differentiable structure of K is characterized.

Semigroup Analysis of Structured Parasite Populations

J. Z. Farkas, D. M. Green, P. Hinow (2010)

Mathematical Modelling of Natural Phenomena

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...

Semigroup commutators under differences (II).

Nicholas Th. Varopoulos (1993)

Revista Matemática Iberoamericana

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...

Semi-groupes d'opérateurs invariants et opérateurs dissipatifs invariants

Jacques Faraut, Khelifa Harzallah (1972)

Annales de l'institut Fourier

Soit X un espace riemannien symétrique et C 0 ( X ) l’espace des fonctions continues sur X tendant vers 0 à l’infini. On démontre qu’un opérateur ( D A ' , A ) , invariant par les isométries de X , engendre un semi-groupe fortement continu de contractions sur C 0 ( X ) s’il est dissipatif et si son domaine contient les fonctions de classe 𝒞 à support compact.

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