Abstract: Kinetic equations often contain uncertain parameters due to inaccurate measurement or empirical constitutive relations. A proper quantification of uncertainties is therefore of practical importance to obtain reliable predictions to solutions of such equations. In this talk we provide a general framework of quantifying the effect of uncertainty in kinetic equations that embrace multiple scales. We show that, the regularity of the solution does not depend on specific form of the collision term, the probability distribution of the random variables, or the regimes the system sets in. This result is important for the success of numerical methods such as stochastic Galerkin/collocation method
Biography: Dr. Li Wang is an Assistant Professor in the Department of Mathematics at the University of Buffalo starting Jan. 2016. She is also a core faculty member of the Computational and Data-Enabled Science and Engineering program. Before joining UB, Dr. Wang was a CAM Assistant Adjunct Professor at UCLA Math Department after received her Ph.D. at the University of Wisconsin—Madison in 2012. Her research mainly includes numerical analysis, mathematical modeling and applied analysis for problems arising from conservation laws, kinetic theory, quantum mechanics and etc. More recently she is also working on uncertainty quantification for kinetic equations, inverse radiative transfer and computational optimal transport.