SEMINARI DI ANALISI MATEMATICA
- Monotone and concave nonautonomous dynamical systems
- 19.02.2013 14.30 h
- Palazzo Campana - Torino
- Aula S
- Prof.ssa Carmen Nunez
- Universidad de Valladolid
- W. Dambrosio
The dynamics of monotone and concave skew-product semiflows is analyzed.
The main goal is to describe the long-term behavior of the semiorbits starting above a semicontinuous subequilibrium and the number and stability properties of the minimal sets.
Several possibilities arise depending on the existence or absence of minimal sets strongly above the subequilibrium and the coexistence or not of bounded and unbounded semiorbits. The analysis is more exhaustive in the case that the scenario comes from a two dimensional system of nonautonomous differential equations, of ordinary, finite-delay or parabolic type.
Under the assumption of the existence of a semicontinuous subequilibrium (or, roughly speaking, of a semicontinuous lower-solution) and of a minimal set situated strongly above it, the behavior of the bounded semiorbits, and the possible shape of the set of all the minimal sets, are described. The results extend and unify previously known properties, showing scenarios which are impossible in the autonomous or periodic cases.
The differences with the sublinear case are quite significative.
- Palazzo Campana - Sito web
- Via Carlo Alberto, 10
Dipartimento di Matematica, Università degli Studi di Torino