4 papers
Long- and short-time behavior of hypocoercive evolution equations via modal decompositions
F. Achleitner, A. Arnold, V. Mehrmann +1
The long- and short-time behavior of solutions to dissipative evolution equations is studied by applying the concept of hypocoercivity. Aiming at partial differential equations tha…
Fractional Dissipative PDEs
Franz Achleitner, Goro Akagi, Christian Kuehn +4
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we…
Hypocoercivity for Linear ODEs and Strong Stability for Runge--Kutta Methods
Franz Achleitner, Anton Arnold, Ansgar Jüngel
In this note, we connect two different topics from linear algebra and numerical analysis: hypocoercivity of semi-dissipative matrices and strong stability for explicit Runge--Kutta…
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…