Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4182
 Publisher DOI: 10.1007/978-3-030-89397-2_16 Title: Non-autonomous evolutionary equations Language: English Authors: Seifert, Christian  Trostorff, Sascha Waurick, Marcus Issue Date: 28-Sep-2021 Publisher: Springer Source: Operator Theory: Advances and Applications 287: 259-273 (2022-01-01) Abstract (english): Previously, 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. URI: http://hdl.handle.net/11420/11756 DOI: 10.15480/882.4182 ISBN: 978-3-030-89397-2978-3-030-89396-5 Institute: Mathematik E-10 Document Type: Chapter (Book) License: CC BY 4.0 (Attribution) Part of Series: Operator theory Volume number: 287 Appears in Collections: Publications with fulltext

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