Homogenization in fractional elasticity

Marcus Waurick

doi:10.1137/130941596

Homogenization in fractional elasticity

Marcus Waurick

Mathematics And Statistics

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

29 Citations (Scopus)

Abstract

In this note we treat the equations of fractional elasticity. After establishing wellposedness, we show a compactness result related to the theory of homogenization. For this, a previous result in (abstract) homogenization theory of evolutionary equations has to be improved. The approach also permits the consideration of nonlocal operators (in time and space).

Original language	English
Pages (from-to)	1551-1576
Number of pages	26
Journal	SIAM Journal on Mathematical Analysis
Volume	46
Issue number	2
DOIs	https://doi.org/10.1137/130941596
Publication status	Published - 10 Apr 2014

Keywords

delay and memory effects
fractional derivatives
G-convergence
homogenization
partial differential equations

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10.1137/130941596

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abstract = "In this note we treat the equations of fractional elasticity. After establishing wellposedness, we show a compactness result related to the theory of homogenization. For this, a previous result in (abstract) homogenization theory of evolutionary equations has to be improved. The approach also permits the consideration of nonlocal operators (in time and space).",

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author = "Marcus Waurick",

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N2 - In this note we treat the equations of fractional elasticity. After establishing wellposedness, we show a compactness result related to the theory of homogenization. For this, a previous result in (abstract) homogenization theory of evolutionary equations has to be improved. The approach also permits the consideration of nonlocal operators (in time and space).

AB - In this note we treat the equations of fractional elasticity. After establishing wellposedness, we show a compactness result related to the theory of homogenization. For this, a previous result in (abstract) homogenization theory of evolutionary equations has to be improved. The approach also permits the consideration of nonlocal operators (in time and space).

KW - delay and memory effects

KW - fractional derivatives

KW - G-convergence

KW - homogenization

KW - partial differential equations

UR - http://epubs.siam.org/journal/sjmaah

U2 - 10.1137/130941596

DO - 10.1137/130941596

M3 - Article

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VL - 46

SP - 1551

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 2

ER -

Homogenization in fractional elasticity

Abstract

Keywords

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