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Zeitschrift für Analysis und ihre Anwendungen

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Volume 33, Issue 4, 2014, pp. 385–415
DOI: 10.4171/ZAA/1518

Published online: 2014-10-15

$G$-Convergence of Linear Differential Equations

Marcus Waurick[1]

(1) Technische Universität Dresden, Germany

We discuss $G$-convergence of linear integro-di erential-algebraic equations in Hilbert spaces. We show under which assumptions it is generic for the limit equation to exhibit memory e ects. Moreover, we investigate which classes of equations are closed under the process of $G$-convergence. The results have applications to the theory of homogenization. As an example we treat Maxwell's equation with the Drude-Born-Fedorov constitutive relation.

Keywords: $G$-convergence, integro-differential-algebraic equations, homogenization, integral equations, Maxwell's equations

Waurick Marcus: $G$-Convergence of Linear Differential Equations. Z. Anal. Anwend. 33 (2014), 385-415. doi: 10.4171/ZAA/1518