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Abstract: We provide a mathematical analysis for the appearance of concentrations (as Dirac masses) in the solutions to Fokker-Planck systems with asymmetric potentials. This problem has been proposed as a model to describe motor proteins moving along molecular filaments. The components of the system describe the densities of the different conformations of the proteins. Our results are based on the study of a Hamilton-Jacobi equation arising, at the zero diffusion limit, after an exponential transformation change of the phase function that yields a viscous Hamilton-Jacobi equation. We consider different classes of conformation transitions coefficients (bounded, unbounded and locally vanishing).
Mots Clés: Hamilton-Jacobi equations; molecular motors; Fokker-Planck equations