Semiclassical Resonances and trace formulae for non-semi-bounded Hamiltonians
Let Ω be a measure space, and E, F be separable Banach spaces. Given a multifunction , denote by the set of all measurable selections of the multifunction , s ↦ f(s,x(s)), for a function x: Ω → E. First, we obtain new theorems on H-upper/H-lower/lower semicontinuity (without assuming any conditions on the growth of the generating multifunction f(s,u) with respect to u) for the multivalued (Nemytskiĭ) superposition operator mapping some open domain G ⊂ X into , where X and Y are Köthe-Bochner...
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...
Un problema di Stefan a due fasi con condizione di flusso non lineare sulla parte fissa della frontiera è affrontato mediante la teoria dei semigruppi di contrazione in . Si dimostra l'esistenza e l’unicità della soluzione nel senso di Crandall-Liggett e Bénilan.
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...