4 papers
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…
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…
Existence of undercompressive travelling waves of a non-local generalised Korteweg-de Vries-Burgers equation
F. Achleitner, C. M. Cuesta, X. Diez-Izagirre
We study travelling wave solutions of a generalised Korteweg-de Vries-Burgers equation with a non-local diffusion term and a concave-convex flux. This model equation arises in the…