Homogenization in fractional elasticity. (English) Zbl 1348.74291
Summary: 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 [the author, Asymptotic Anal. 82, No. 3–4, 271–294 (2013; Zbl 1280.35152)] in (abstract) homogenization theory of evolutionary equations has to be improved. The approach also permits the consideration of nonlocal operators (in time and space).
MSC:
74Q10 | Homogenization and oscillations in dynamical problems of solid mechanics |
74B99 | Elastic materials |
35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
35Q74 | PDEs in connection with mechanics of deformable solids |
26A33 | Fractional derivatives and integrals |