Contributions to Books:
F. Achleitner, A. Arnold, B. Signorello:
"On optimal decay estimates for ODEs and PDEs with modal decomposition";
in: "ASC Report 4/2018",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
We consider the Goldstein-Taylor model, which is a 2-velocity
BGK model, and construct the "optimal" Lyapunov functional to quan-tify the convergence to the unique normalized steady state. The Lya-punov functional is optimal in the sense that it yields decay estimates in L2-norm with the sharp exponential decay rate and minimal multiplica-tive constant. The modal decomposition of the Goldstein-Taylor model leads to the study of a family of 2-dimensional ODE systems. Therefore we discuss the characterization of "optimal" Lyapunov functionals for linear ODE systems with positive stable diagonalizable matrices. We give a complete answer for 2-dimensional ODE systems, and a partial answer for higher dimensional ODE systems.
Lyapunov functionals, sharp decay estimates, Goldstein-Taylor model.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.