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math.AP2025
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…
math.AP2025
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…
math.AP2024
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…