Oradores/Speakers: Nicolae Lupa (Politehnica University of Timisoara) and Mihail Megan (West University of Timisoara)

Data, hora e local: 23 de junho de 2016, às 15h na sala de reuniões do DMUBI.

Resumo/Abstract: For nonuniform exponentially bounded evolution families on the half-line we introduce a class of Banach function spaces on which we define nonuniform evolution semi-groups. We completely characterize nonuniform exponential stability in terms of invertibility of the corresponding generators. Our main goal is to emphasize an important diference between uniform and nonuniform behavior: while in the uniform case all the evolution families reflect into a unique output function space (of functions vanishing at 0 and infinity, for instance), in the nonuniform case there are infinitely many output function spaces. We emphasize that in particular our results apply to all linear differential equations with bounded operator and finite Lyapunov exponent.

Funded by the Portuguese Government through the FCT – Fundação para a Ciência e a Tecnologia under the project UID/MAT/00212/2013