G-convergence of linear differential equations

Marcus Waurick

doi:10.4171/ZAA/1518

G-convergence of linear differential equations

Marcus Waurick

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We discuss GG-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 GG-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.

Original language	English
Pages (from-to)	385-415
Number of pages	31
Journal	Journal of Analysis and its Applications
Volume	33
Issue number	4
DOIs	https://doi.org/10.4171/ZAA/1518
Publication status	Published - 2014

Keywords

G-convergence
integro-differential-algebraic equations
homogenization
integral equations
Maxwell's equations

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10.4171/ZAA/1518

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title = "G-convergence of linear differential equations",

abstract = "We discuss GG-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 GG-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.",

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author = "Marcus Waurick",

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PY - 2014

Y1 - 2014

N2 - We discuss GG-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 GG-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.

AB - We discuss GG-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 GG-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.

KW - G-convergence

KW - integro-differential-algebraic equations

KW - homogenization

KW - integral equations

KW - Maxwell's equations

UR - http://www.ems-ph.org/journals/journal.php?jrn=zaa

U2 - 10.4171/ZAA/1518

DO - 10.4171/ZAA/1518

M3 - Article

SN - 0232-2064

VL - 33

SP - 385

EP - 415

JO - Journal of Analysis and its Applications

JF - Journal of Analysis and its Applications

IS - 4

ER -

G-convergence of linear differential equations

Abstract

Keywords

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