2017/06/09 by Kirill Cherednichenko, Cherednichenko, Kirill, Marcus Waurick +1
Computer Science · Engineering · Mathematics · #34K08 #34K37 #35B27 #74D10 #74Q10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #math.AP #math.FA #msc:34K08 #msc:34K37 #msc:35B27 #msc:74D10 #msc:74Q10
paper · pdf · doi:10.48550/arxiv.1706.02988
22 pages
arxiv created 2017/06/09 · openalex publication_date 2017/06/09 · arxiv updated 2017/06/12 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28
We provide operator-norm convergence estimates for solutions to a time-dependent equation of fractional elasticity in one spatial dimension, with rapidly oscillating coefficients that represent the material properties of a viscoelastic composite medium. Assuming periodicity in the coefficients, we prove operator-norm convergence estimates for an operator fibre decomposition obtained by applying to the original fractional elasticity problem the Fourier--Laplace transform in time and Gelfand transform in space. We obtain estimates on each fibre that are uniform in the quasimomentum of the decomposition and in the period of oscillations of the coefficients as well as quadratic with respect to the spectral variable. On the basis of these uniform estimates we derive operator-norm-type convergence estimates for the original fractional elasticity problem, for a class of sufficiently smooth densities of applied forces.