On optimal decay estimates for ODEs and PDEs with modal decomposition

29 Sep 2020 Achleitner Franz Arnold Anton Signorello Beatrice

We consider the Goldstein-Taylor model, which is a 2-velocity BGK model, and construct the "optimal" Lyapunov functional to quantify the convergence to the unique normalized steady state. The Lyapunov functional is optimal in the sense that it yields decay estimates in $L^2$-norm with the sharp exponential decay rate and minimal multiplicative constant... (read more)

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