Homogenization and propagation of chaos to a nonlinear diffusion with sticky reflection |
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Authors: | Carl Graham |
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Institution: | (1) Centre de Mathématiques Appliquées, Ecole Polytechnique URA CNRS 756, F-91128 Palaiseau, France |
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Abstract: | Summary We study a process reflecting in a domain. The process follows Wentzell non-sticky boundary conditions while being adsorbed at the boundary at a certain rate with respect to local time and desorbed at a rate with respect to natural time. We show that when the rates go to infinity with a converging ratio, the process converges to a process with sticky reflection having the limit ratio as the sojourn coefficient. We then study a mean-field interacting system of such particles. We show propagation of chaos to a nonlinear diffusion with sticky reflection when we perform this homogenization simultaneously as the number of particles goes to infinity. |
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Keywords: | 60F17 60K35 35K60 |
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