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Article Dans Une Revue Electronic Journal of Probability Année : 2023

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

Ellen Saada
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Sonia Velasco
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Résumé

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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Dates et versions

hal-03897093 , version 1 (14-12-2022)
hal-03897093 , version 2 (06-07-2023)
hal-03897093 , version 3 (20-10-2023)

Identifiants

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Mustapha Mourragui, Ellen Saada, Sonia Velasco. Hydrodynamic and hydrostatic limit for a generalized contact process with mixed boundary conditions. Electronic Journal of Probability, 2023, Electron. J. Probab. (28), pp.1-44. ⟨10.1214/23-EJP1025⟩. ⟨hal-03897093v3⟩
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