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.
Keywords: Interacting particle system, stochastic processes, mean-field equations, hydrodynamic limit, numerical simulations
Chen, Li 1 ; Göttlich, Simone 1 ; Knapp, Stephan 1
@article{M2AN_2018__52_2_567_0,
author = {Chen, Li and G\"ottlich, Simone and Knapp, Stephan},
title = {Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {567--593},
year = {2018},
publisher = {EDP Sciences},
volume = {52},
number = {2},
doi = {10.1051/m2an/2018028},
zbl = {1404.35434},
mrnumber = {3834436},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2018028/}
}
TY - JOUR AU - Chen, Li AU - Göttlich, Simone AU - Knapp, Stephan TI - Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 567 EP - 593 VL - 52 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2018028/ DO - 10.1051/m2an/2018028 LA - en ID - M2AN_2018__52_2_567_0 ER -
%0 Journal Article %A Chen, Li %A Göttlich, Simone %A Knapp, Stephan %T Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 567-593 %V 52 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2018028/ %R 10.1051/m2an/2018028 %G en %F M2AN_2018__52_2_567_0
Chen, Li; Göttlich, Simone; Knapp, Stephan. Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 2, pp. 567-593. doi: 10.1051/m2an/2018028
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