33 citations · 200 across the 20 of their papers we have counts for
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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…
Hypocoercivity in Hilbert spaces
Franz Achleitner, Anton Arnold, Volker Mehrmann +1
The concept of hypocoercivity for linear evolution equations with dissipation is discussed and equivalent characterizations that were developed for the finite-dimensional case are…
Hypocoercivity and hypocontractivity concepts for linear dynamical systems
Franz Achleitner, Anton Arnold, Volker Mehrmann
For linear dynamical systems (in continuous-time and discrete-time) we revisit and extend the concepts of hypocoercivity and hypocontractivity and give a detailed analysis of the r…
The hypocoercivity index for the short time behavior of linear time-invariant ODE systems
Franz Achleitner, Anton Arnold, Eric A. Carlen
We consider the class of conservative-dissipative ODE systems, which is a subclass of Lyapunov stable, linear time-invariant ODE systems. We characterize asymptotically stable, con…
Metastable Speeds in the Fractional Allen-Cahn Equation
Franz Achleitner, Christian Kuehn, Jens Markus Melenk +1
We study numerically the one-dimensional Allen-Cahn equation with the spectral fractional Laplacian on intervals with homogeneous Neumann boundary conditions. In parti…