Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2014-10-15
$G$-Convergence of Linear Differential EquationsMarcus Waurick (1) Technische Universität Dresden, Germany
We discuss $G$-convergence of linear integro-dierential-algebraic equations in Hilbert spaces. We show under which assumptions it is generic for the limit equation to exhibit memory eects. 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