12 citations · 29 across the 21 of their papers we have counts for
23 papers
Positivity and long-term behaviour of a diffusion model with measure-valued nonlocal reaction term
Xiao Yang, Qiyao Peng, Sander C. Hille
The behaviour is investigated of solutions to a diffusion equation on the real line with nonlocal and singular reaction term, i.e., given by a Dirac source or sink at the origin. I…
Law of the Iterated Logarithm for Markov Semigroups with Exponential Mixing in the Wasserstein Distance
Dawid Czapla, Sander C. Hille, Katarzyna Horbacz +1
In this paper, we establish the law of the iterated logarithm for a wide class of non-stationary, continuous-time Markov processes evolving on Polish spaces. Specifically, our resu…
Approximating a spatially-heterogeneously mass-emitting object by multiple point sources in a diffusion model
Qiyao Peng, Sander C. Hille
Various biological cells secrete diffusing chemical compounds into their environment for communication purposes. Secretion usually takes place over the cell membrane in a spatially…
Invariance properties of the solution operator for measure-valued semilinear transport equations
Sander C. Hille, Rainey Lyons, Adrian Muntean
We provide conditions under which we prove for measure-valued transport equations with non-linear reaction term in the space of finite signed Radon measures, that positivity is pre…
Unique ergodicity for noninvertible function systems on an interval
Sander C. Hille, Hanna Oppelmayer, Tomasz Szarek
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these sys…
Approximation of a compound-exchanging cell by a Dirac point
Xiao Yang, Qiyao Peng, Sander C. Hille
Communication between single cells or higher organisms by means of diffusive compounds is an important phenomenon in biological systems. Modelling therefore often occurs, most stra…