Homogenization in fractional elasticity

2013/02/07 by Marcus Waurick, Waurick, Marcus
Computer Science · Engineering · Mathematics · #35B27 #35Q74 #74Q15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #math.AP #math.FA #msc:35B27 #msc:35Q74 #msc:74Q15

paper · pdf · doi:10.48550/arxiv.1302.1731

35 pages; thoroughly revised version with more detailed proofs

openalex publication_date 2013/02/07 · arxiv created 2013/09/18 · arxiv updated 2013/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we treat the equations of fractional elasticity. After establishing well-posedness, 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 non-local operators (in time and space).

Related

• A Note on Fractional Evolutionary Equations
• On the simultaneous homogenization and dimension reduction in elasticity and locality of Γ-closure
• Resolvent estimates in homogenisation of periodic problems of fractional elasticity
• From nonlocal Eringen's model to fractional elasticity
• Upper bounds for the homogenization problem in nonlinear elasticity: the incompressible case