Projects per year
Abstract
We provide operatornorm convergence estimates for solutions to a timedependent 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 operatornorm 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 operatornormtype convergence estimates for the original fractional elasticity problem, for a class of sufficiently smooth densities of applied forces.
Original language  English 

Pages (fromto)  38113835 
Number of pages  25 
Journal  Journal of Differential Equations 
Volume  264 
Issue number  6 
Early online date  9 Jan 2018 
DOIs  
Publication status  Published  15 Mar 2018 
Keywords
 Fractional elasticity
 Gelfand transform
 Homogenisation
 Operatornorm convergence
 Resolvent estimates
ASJC Scopus subject areas
 Analysis
 Applied Mathematics
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Projects
 3 Finished

Newton Mobility Grant : Homogenisation of Degenerate Equations and Scattering for New Materials
1/02/17 → 31/01/19
Project: Research council

International Research Accelerator Scheme
Shaddick, G., Kyprianou, A., Milewski, P., Cherednichenko, K. & Majumdar, A.
1/09/16 → 1/09/18
Project: Researchrelated funding

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council