Positive irreducible semigroups and their long-time behaviour

W Arendt, J Glück - … Transactions of the Royal Society A, 2020 - royalsocietypublishing.org
The notion Perron–Frobenius theory usually refers to the interaction between three
properties of operator semigroups: positivity, spectrum and long-time behaviour. These …

Locally eventually positive operator semigroups

S Arora - arXiv preprint arXiv:2101.11386, 2021 - arxiv.org
We initiate a theory of locally eventually positive operator semigroups on Banach lattices.
Intuitively this means: given a positive initial datum, the solution of the corresponding …

A criterion for the uniform eventual positivity of operator semigroups

D Daners, J Glück - Integral Equations and Operator Theory, 2018 - Springer
Abstract Consider a C_0 C 0-semigroup (e^ tA) _ t ≥ 0 (e tA) t≥ 0 on a function space or,
more generally, on a Banach lattice E. We prove a sufficient criterion for the operators e^ tA …

Spectrum and convergence of eventually positive operator semigroups

S Arora, J Glück - Semigroup Forum, 2021 - Springer
An intriguing feature of positive C_0 C 0-semigroups on function spaces (or more generally
on Banach lattices) is that their long-time behaviour is much easier to describe than it is for …

Evolution equations with eventually positive solutions

J Glück - European Mathematical Society Magazine, 2022 - ems.press
We discuss linear autonomous evolution equations on function spaces which have the
property that a positive initial value leads to a solution which initially changes sign, but then …

Irreducibility of eventually positive semigroups

S Arora, J Glück - arXiv preprint arXiv:2307.04627, 2023 - arxiv.org
Positive $ C_0 $-semigroups that occur in concrete applications are, more often than not,
irreducible. Therefore a deep and extensive theory of irreducibility has been developed that …

Long-term behaviour of operator semigroups and (anti-) maximum principles

S Arora - 2023 - tud.qucosa.de
Abstract (EN) Combining an idea of Takáč with the techniques of Daners, Glück, and
Kennedy, we investigate individual and uniform (anti-) maximum principles, thereby …

An operator theoretic approach to uniform (anti-) maximum principles

S Arora, J Glück - Journal of Differential Equations, 2022 - Elsevier
Maximum principles and uniform anti-maximum principles are a ubiquitous topic in PDE
theory that is closely tied to the Krein–Rutman theorem and kernel estimates for resolvents …

Local uniform convergence and eventual positivity of solutions to biharmonic heat equations

D Daners, J Glück, J Mui - Differential and Integral Equations, 2023 - projecteuclid.org
We study the evolution equation associated with the biharmonic operator on infinite
cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The …

Towards a perturbation theory for eventually positive semigroups

D Daners, J Glück - Journal of Operator Theory, 2018 - JSTOR
We consider eventually positive operator semigroups and study the question whether their
eventual positivity is preserved by bounded perturbations of the generator or not. We …