Exploring limit behaviour of non-quadratic terms via H-measures. Application to small amplitude homogenisation
Analysis of PDEs
2016-01-27 v2
Abstract
A method is developed for analysing asymptotic behaviour of terms involving an arbitrary integer order powers of L p functions by means of H-measures. It is applied to the small amplitude homogenisation problem for a stationary diffusion equation, in which coefficients are assumed to be analytic perturbations of a constant, enabling formul{\ae} for higher order correction terms in a general, non-periodic setting. Explicit expressions in terms of Fourier coefficients are obtained under periodicity assumption. The method enables its generalisation and application to the corresponding non-stationary equation, as well as to some other small amplitude homogenisation problems.
Keywords
Cite
@article{arxiv.1502.07493,
title = {Exploring limit behaviour of non-quadratic terms via H-measures. Application to small amplitude homogenisation},
author = {Martin Lazar},
journal= {arXiv preprint arXiv:1502.07493},
year = {2016}
}