Exploring limit behaviour of non-quadratic terms via H-measures. Application to small amplitude homogenisation. Issue 16 (10th December 2017)

• Record Type: Journal Article
• Authors: Lazar, Martin
• Is Part Of: Applicable analysis. Volume 96:Issue 16(2017)
• Page Start: 2832
• Page End: 2845
• Publication Date: 2017-12-10
• Subjects: Small amplitude homogenisation -- H-measures -- non-quadratic terms; 35B27 -- 35J15 -- 35S05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1248422
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : A method is developed for analysing asymptotic behaviour of terms involving an arbitrary integer order powers of 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 formulæ 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 allows of its generalisation and application to the corresponding non-stationary equation, as well as to some other small amplitude homogenisation problems.