Sensitivity analysis of the non-linear Fokker–Planck equations with uncertainty. (April 2022) - Liao, Jie; Liu, Hui
Abstract: In this paper, we study sensitivity analysis of the non-linear Fokker–Planck equations with uncertainty. Modeled by random variable, the uncertainty enters the solution through initial data. By deriving Lyapunov-type inequalities, under some smallness assumptions on the initial data, we have the regularity of the solution in the random space. The nonlinearity in the model brings new difficulties to the energy estimates, which is resolved by using careful weighted-in- v energy estimates suitable for Fokker–Planck operators. The analysis is important for understanding of the sensitivity of the system under random perturbations, and for the study of convergence rates of popular numerical methods for uncertainty quantification based on polynomial chaos expansions.