3 papers
math.AP2025
A piston to counteract diffusion: The influence of an inward-shifting boundary on the heat equation in half-space
Samuel Tréton, Mingmin Zhang
To better understand how populations respond to dynamic external pressure, we propose a new diffusion model in the moving half-line {z b(t)}, where the boundary position b(t)…
math.AP2025
The field-road diffusion model: fundamental solution and asymptotic behavior
Matthieu Alfaro, Romain Ducasse, Samuel Tréton
We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. This system takes the form of a system of PDEs set on domains of d…
math.AP2024
Emergence of complexity in opinion propagation: A reaction-diffusion model
Romain Ducasse, Samuel Tréton
We analyze a model designed to describe the spread and accumulation of opinions in a population. Inspired by the social contagion paradigm, our model is built on the classical SIR…