A. Arnold, S. Jin, T. Wöhrer:

"Sharp Decay Estimates in Local Sensitivity Analysis for Evolution Equations with Uncertainties: from ODEs to Linear Kinetic Equations";

in: "ASC Report 08/2019", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2019, ISBN: 978-3-902627-12-4, 1 - 50.

We review the Lyapunov functional method for linear ODEs

and give an explicit construction of such functionals that yields sharp decay estimates, including an extension to defective ODE systems. As an application, we consider three evolution equations, namely the linear convection-diffusion equation, the two velocity BGK model and the Fokker{Planck equation.

Adding an uncertainty parameter to the equations and analyzing its

linear sensitivity leads to defective ODE systems.

long time behavior, defective ODEs, kinetic equations, BGK models, Lyapunov functionals, uncertainty quantification, sensitivity analysis, non-defective limit, Fokker{Planck equations

http://www.asc.tuwien.ac.at/preprint/2019/asc08x2019.pdf

Created from the Publication Database of the Vienna University of Technology.