Uncertainty Quantification in Kinetic Equations

  • The Vlasov Fokker Planck Equation with High Dimensional Parametric Forcing Term. [pdf]

Shi Jin, Yuhua Zhu*, and Enrique Zuazua. 

Numerische Mathematik, 2021.

  • A Local Sensitivity and Regularity Analysis for the Vlasov-Poisson-Fokker-Planck System with Multi-dimensional Uncertainty and the Spectral Convergence of the Stochastic Galerkin Method. [pdf]

Yuhua Zhu. 

Networks and Heterogeneous Media, 14(4), 677-707, 2019.

  • An Uncertainty Quantification Approach to the Study of Gene Expression Robustness. [pdf]

Pierre Degond, Shi Jin and Yuhua Zhu*.

Methods and Applications of Analysis (A special issue in honor of the 80th birthday of Prof. Ling Hsiao), 2019.

  • Hypocoercivity and Uniform Regularity for the Vlasov-Poisson-Fokker-Planck System with Uncertainty and Multiple Scales. [pdf]

Shi Jin and Yuhua Zhu*. 

SIAM Journal on Mathematical Analysis, 50, 1790-1816, 2018.

  • The Vlasov-Poisson-Fokker-Planck System with Uncertainty and a One-Dimensional Asymptotic-Preserving Method. [pdf]

Yuhua Zhu and Shi Jin.

Multiscale Modeling and Simulation, 15, 1502-1529, 2018.

  • Stabilization of the Vlasov Fokker Planck Equation with Reflective Boundary Condition. [pdf]

Michael Herty, Shi Jin and Yuhua Zhu*.

Preprint.