Geodesic
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

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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.

DOI : 10.1051/m2an/2018028
Classification : 35Q70, 82C22, 65M06
Keywords: Interacting particle system, stochastic processes, mean-field equations, hydrodynamic limit, numerical simulations

Chen, Li 1 ; Göttlich, Simone 1 ; Knapp, Stephan 1

1 
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     title = {Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {567--593},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {2},
     year = {2018},
     doi = {10.1051/m2an/2018028},
     zbl = {1404.35434},
     mrnumber = {3834436},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2018028/}
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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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