Resolvent estimates in homogenisation of periodic problems of fractional elasticity

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Cherednichenko, Kirill¹  Waurick, Marcus^1,2 

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] Univ Strathclyde, Dept Math & Stat, Livingstone Tower,26 Richmond St, Glasgow G1 1XH, Lanark, Scotland

关键词: Fractional elasticity;    Homogenisation;    Gelfand transform;    Operator-norm convergence;    Resolvent estimates;   

DOI  :  10.1016/j.jde.2017.11.038

来源: Elsevier

【 摘 要 】

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. (C) 2018 The Authors. Published by Elsevier Inc.

【 授权许可】

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