Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4178
 Publisher DOI: 10.1007/978-3-030-89397-2_10 Title: Differential algebraic equations Language: English Authors: Seifert, Christian  Trostorff, Sascha Waurick, Marcus Issue Date: 28-Sep-2021 Publisher: Springer Source: Operator Theory: Advances and Applications 287: 149-165 (2022-01-01) Abstract (english): Let H be a Hilbert space and ν∈ ℝ. We saw in the previous chapter how initial value problems can be formulated within the framework of evolutionary equations. More precisely, we have studied problems of the form {(∂t,νM0+M1+A)U=0on(0,∞),M0U(0+)=M0U0 \displaystyle \begin{aligned} \begin {cases} \left (\partial _{t,\nu }M_{0}+M_{1}+A\right )U=0 & \text{ on }\left (0,\infty \right ),\\ M_{0}U(0{\scriptstyle {+}})=M_{0}U_{0} \end {cases} \end{aligned} for U0 ∈ H, M0, M1 ∈ L(H) and A: dom (A) ⊆ H→ H skew-selfadjoint; that is, we have considered material laws of the form M(z): =M0+z−1M1(z∈ℂ∖{0}). $$\displaystyle M(z)\mathrel{\mathop:}= M_{0}+z^{-1}M_{1}\quad (z\in \mathbb {C}\setminus \{0\}).$$ URI: http://hdl.handle.net/11420/11752 DOI: 10.15480/882.4178 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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