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 first show that when the system is in contact with reservoirs at different slow-down rates, the hydrodynamic limit is a set of coupled non linear reaction-diffusion equations with mixed boundary conditions. We then prove the hydrostatic limit when the macroscopic equations exhibit a unique attractor.
Acknowledgments
We thank the anonymous referees for their careful reading of the paper and comments which allowed to notably improve it. The authors would also like to thank Frank Redig for an interesting discussion as well as Camille Pouchol for some useful advice regarding numerical simulations. This work has been conducted within the FP2M federation (CNRS FR 2036).
Citation
Mustapha Mourragui. Ellen Saada. Sonia Velasco. "Hydrodynamic and hydrostatic limit for a generalized contact process with mixed boundary conditions." Electron. J. Probab. 28 1 - 44, 2023. https://doi.org/10.1214/23-EJP1025
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