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math.AP2018
Large-time asymptotics of a fractional drift-diffusion-Poisson system via the entropy method
Franz Achleitner, Ansgar Jüngel, Masakazu Yamamoto
The self-similar asymptotics for solutions to the drift-diffusion equation with fractional dissipation, coupled to the Poisson equation, is analyzed in the whole space. It is shown…
math.AP2018★ 13 cited
On optimal decay estimates for ODEs and PDEs with modal decomposition
Franz Achleitner, Anton Arnold, Beatrice Signorello
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…