Eventually Positive Semigroups

Daniel Daners
University of Sydney
Mon 15 September 2014 2-3pm, Carslaw 829 (AGR)

Abstract

We consider one-parameter semigroups of linear operators $e^{tA}$ on $C\left(K\right)$ such that for every $f>0$ there exists $t_0>0$ so that $e^{tA}f>0$ for all $t>t_0$. The purpose of the talk is to give a general theory of such eventually positive semigroups and characterise them in terms of positivity properties of the resolvent ${\left(\lambda I-A\right)}^{-1}$ and the spectral projection associated with the spectral bound.

Examples of eventually positive semigroups include the semigroup generated by the Dirichlet-to-Neumann operator, delay differential equations, higher order parabolic equations and some matrix semigroups.

This is joint work with Wolfgang Arendt, Jochen Glück and James Kennedy.

Check also the PDE Seminar page. Enquiries to Daniel Hauer or Daniel Daners.