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arXiv · 2212.07762

Hydrodynamic and hydrostatic limit for a generalized contact process with mixed boundary conditions

Mustapha Mourragui·Ellen Saada·Sonia Velasco
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Abstract

We consider an interacting particle system which models the sterile insect technique. It is the superposition of a generalized contact process with exchanges of particles on a finite cylinder with open boundaries (see Kuoch et al., 2017). We show that when the system is in contact with reservoirs at different slowdown rates, the hydrodynamic limit is a set of coupled non linear reaction-diffusion equations with mixed boundary conditions. We also prove the hydrostatic limit when the macroscopic equations exhibit a unique attractor.

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Mustapha Mourragui, Ellen Saada, Sonia Velasco. 2022-12-15. Hydrodynamic and hydrostatic limit for a generalized contact process with mixed boundary conditions. https://arxiv.org/abs/2212.07762

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