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 …
properties of operator semigroups: positivity, spectrum and long-time behaviour. These …
Almost Interior Points in Ordered Banach Spaces and the Long--Term Behaviour of Strongly Positive Operator Semigroups
J Glück, MR Weber - arXiv preprint arXiv:1901.03306, 2019 - arxiv.org
The first part of this article is a brief survey of the properties of so-called almost interior points
in ordered Banach spaces. Those vectors can be seen as a generalization of``functions …
in ordered Banach spaces. Those vectors can be seen as a generalization of``functions …
Asymptotic properties of a general model of immune status
K Pichór, R Rudnicki - SIAM Journal on Applied Mathematics, 2023 - SIAM
We consider a model of dynamics of the immune system. The model is based on three
factors: occasional boosting and continuous waning of immunity and a general description …
factors: occasional boosting and continuous waning of immunity and a general description …
On the quasi-ergodicity of absorbing Markov chains with unbounded transition densities, including random logistic maps with escape
In this paper, we consider absorbing Markov chains $ X_n $ admitting a quasi-stationary
measure $\mu $ on M where the transition kernel ${\mathcal P} $ admits an eigenfunction …
measure $\mu $ on M where the transition kernel ${\mathcal P} $ admits an eigenfunction …
Analytic solutions for stochastic hybrid models of gene regulatory networks
Discrete-state stochastic models are a popular approach to describe the inherent
stochasticity of gene expression in single cells. The analysis of such models is hindered by …
stochasticity of gene expression in single cells. The analysis of such models is hindered by …
Cell cycle length and long‐time behavior of an age‐size model
K Pichór, R Rudnicki - Mathematical Methods in the Applied …, 2022 - Wiley Online Library
We consider an age‐size structured cell population model based on the cell cycle length.
The model is described by a first order partial differential equation with initial‐boundary …
The model is described by a first order partial differential equation with initial‐boundary …
Uniform convergence of stochastic semigroups
J Glück, FG Martin - Israel Journal of Mathematics, 2022 - Springer
For stochastic C 0-semigroups on L 1-spaces there is a wealth of results that show strong
convergence to an equilibrium as t→∞, given that the semigroup contains a partial integral …
convergence to an equilibrium as t→∞, given that the semigroup contains a partial integral …
[HTML][HTML] On a convergence theorem for semigroups of positive integral operators
We give a new and very short proof of a theorem of Greiner asserting that a positive and
contractive C 0-semigroup on an L p-space is strongly convergent in case it has a strictly …
contractive C 0-semigroup on an L p-space is strongly convergent in case it has a strictly …
Open problems in one-parameter operator semigroups theory
One-parameter strongly continuous semigroups of linear bounded operators in Banach
spaces (also known as $ C_0 $-semigroups) is a fundamental operator-theoretic tool used …
spaces (also known as $ C_0 $-semigroups) is a fundamental operator-theoretic tool used …
On convergence and asymptotic behaviour of semigroups of operators
A Bobrowski, R Rudnicki - Philosophical Transactions of …, 2020 - royalsocietypublishing.org
On convergence and asymptotic behaviour of semigroups of operators | Philosophical
Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences logo logo …
Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences logo logo …