Long- and short-time behavior of hypocoercive evolution equations via modal decompositions

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 that allow for a modal decomposition, we compute estimates that are uniform with respect to all modes. While the special example of the kinetic Lorentz equation was treated in previous work of the authors, that analysis is generalized here to general evolution equations having a scaled family of generators.