**SMS scnews item created by Daniel Daners at Fri 12 Sep 2014 2254**

Type: Seminar

Distribution: World

Expiry: 15 Sep 2014

**Calendar1: 15 Sep 2014 1400-1500**

**CalLoc1: AGR Carslaw 829**

Auth: daners@d58-110-193-163.mas800.nsw.optusnet.com.au (ddan2237) in SMS-WASM

### PDE Seminar

# Eventually Positive Semigroups

### Daners

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.