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Uncertainty Quantification for Kinetic Equations

  • Jingwei Hu
  • Shi JinEmail author
Chapter
Part of the SEMA SIMAI Springer Series book series (SEMA SIMAI, volume 14)

Abstract

Kinetic equations contain uncertainties in their collision kernels or scattering coefficients, initial or boundary data, forcing terms, geometry, etc. Quantifying the uncertainties in kinetic models have important engineering and industrial applications. In this article we survey recent efforts in the study of kinetic equations with random inputs, including their mathematical properties such as regularity and long-time behavior in the random space, construction of efficient stochastic Galerkin methods, and handling of multiple scales by stochastic asymptotic-preserving schemes. The examples used to illustrate the main ideas include the random linear and nonlinear Boltzmann equations, linear transport equation and the Vlasov-Poisson-Fokker-Planck equations.

Notes

Acknowledgements

J. Hu’s research was supported by NSF grant DMS-1620250 and NSF CAREER grant DMS-1654152. S. Jin’s research was supported by NSF grants DMS-1522184 and DMS-1107291: RNMS KI-Net, NSFC grant No. 91330203, and the Office of the Vice Chancellor for Research and Graduate Education at the University of Wisconsin-Madison with funding from the Wisconsin Alumni Research Foundation.

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Authors and Affiliations

  1. 1.Department of MathematicsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA
  3. 3.Department of Mathematics, Institute of Natural Sciences, MOE-LSEC and SHL-MACShanghai Jiao Tong UniversityShanghaiChina

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