| Autor: |
Raveendran, Vishnu, de Bonis, Ida, Cirillo, Emilio N. M., Muntean, Adrian |
| Zdroj: |
Quarterly of Applied Mathematics; Mar2025, Vol. 83 Issue 1, p19-57, 39p |
| Abstrakt: |
We study the periodic homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary condition posed in an unbounded perforated domain. The nonlinear problem is associated with the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. We are interested in deriving rigorously the upscaled model equations and the corresponding effective coefficients for the case when the microscopic dynamics are linked to a particular choice of characteristic length and time scales that lead to an exploding nonlinear drift. The main mathematical difficulty lies in proving the two-scale compactness and strong convergence results needed for the passage to the homogenization limit. To cope with the situation, we use the concept of two-scale compactness with drift, which is similar to the more classical two-scale compactness result but it is defined now in moving coordinates. We provide as well a strong convergence result for the corrector function, starting this way the search for the order of the convergence rate of the homogenization process for our target nonlinear drift problem. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Supplemental Index |
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