Exploring limit behaviour of non-quadratic terms via H-measures. Application to small amplitude homogenisation

Martin Lazar

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arXiv · 1502.07493

Exploring limit behaviour of non-quadratic terms via H-measures. Application to small amplitude homogenisation

Martin Lazar

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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.

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Martin Lazar. 2015-02-26. Exploring limit behaviour of non-quadratic terms via H-measures. Application to small amplitude homogenisation. https://arxiv.org/abs/1502.07493

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