Nonuniform evolution semigroups and exponential stability of evolution families on the half-line

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 dif erence 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 di fferential 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


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