| Issue |
ESAIM: M2AN
Volume 52, Number 2, March–April 2018
|
|
|---|---|---|
| Page(s) | 567 - 593 | |
| DOI | https://doi.org/10.1051/m2an/2018028 | |
| Published online | 11 July 2018 | |
Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation★
University of Mannheim, Department of Mathematics,
68131
Mannheim, Germany.
* Corresponding author: e-mail: goettlich@uni-mannheim.de
Received:
26
January
2018
Accepted:
1
May
2018
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.
Mathematics Subject Classification: 35Q70 / 82C22 / 65M06
Key words: Interacting particle system / stochastic processes / mean-field equations / hydrodynamic limit / numerical simulations
© EDP Sciences, SMAI 2018
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