Seifert, ChristianChristianSeifertTrostorff, SaschaSaschaTrostorffWaurick, MarcusMarcusWaurick2022-02-282022-02-282022Operator Theory: Advances and Applications 287: 259-273 (2022)http://hdl.handle.net/11420/11756Previously, we focussed on evolutionary equations of the form (∂t,νM(∂t,ν)+A¯)U=F. $$\displaystyle \left (\overline {\partial _{t,\nu }M(\partial _{t,\nu })+A}\right )U=F. $$ In this chapter, where we turn back to well-posedness issues, we replace the material law operator M(∂t,ν), which is invariant under translations in time, by an operator of the form ℳ+∂t,ν−1N, $$\displaystyle \mathcal {M}+\partial _{t,\nu }^{-1}\mathcal {N}, $$ where both ℳ and N are bounded linear operators in L2,ν(ℝ; H). Thus, it is the aim in the following to provide criteria on ℳ and N under which the operator ∂t,νℳ+N+A $$\displaystyle \partial _{t,\nu }\mathcal {M}+\mathcal {N}+A $$ is closable with continuous invertible closure in L2,ν(ℝ; H). In passing, we shall also replace the skew-selfadjointness of A by a suitable real part condition. Under additional conditions on ℳ and N, we will also see that the solution operator is causal. Finally, we will put the autonomous version of Picard’s theorem into perspective of the non-autonomous variant developed here.enhttps://creativecommons.org/licenses/by/4.0/MathematikBook Part10.15480/882.418210.1007/978-3-030-89397-2_1610.15480/882.4182Book Chapter