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arXiv · 1801.09074

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

Li Chen·Simone Göttlich·Stephan Knapp
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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.

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Li Chen, Simone Göttlich, Stephan Knapp. 2018-01-27. Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation. https://doi.org/10.1051/m2an/2018028

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