Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation

Abstract

In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a stochastic particle system while introducing an intermediate particle system with smooth interaction potential. The theoretical results are compared to numerical simulations relying on suitable discretization schemes for the microscopic and macroscopic level. In particular, the regime switch where the analytic theory fails is numerically analyzed very carefully and allows for a better understanding of the equation.

25 pages

References in corpus (1)

• Microscopic derivation of the Keller-Segel equation in the sub-critical regime

Cited by in corpus (3)

• Rigorous mean-field limit and cross diffusion
• Rigorous derivation of population cross-diffusion systems from moderately interacting particle systems
• On a class of reaction-diffusion equations with aggregation