Seifert, ChristianChristianSeifertTrostorff, SaschaSaschaTrostorffWaurick, MarcusMarcusWaurick2022-02-242022-02-242022Operator Theory: Advances and Applications 287: 167-188 (2022)http://hdl.handle.net/11420/11753In this chapter we study the exponential stability of evolutionary equations. Roughly speaking, exponential stability of a well-posed evolutionary equation (∂t,νM(∂t,ν)+A)U=F (∂ t,ν M(∂ t,ν )+A)U=F means that exponentially decaying right-hand sides F lead to exponentially decaying solutions U. The main problem in defining the notion of exponential decay for a solution of an evolutionary equation is the lack of continuity with respect to time, so a pointwise definition would not make sense in this framework. Instead, we will use our exponentially weighted spaces L2,ν(ℝ; H), but this time for negative ν, and define the exponential stability by the invariance of these spaces under the solution operator associated with the evolutionary equation under consideration.enhttps://creativecommons.org/licenses/by/4.0/MathematikBook Part10.15480/882.417910.1007/978-3-030-89397-2_1110.15480/882.4179Book Chapter