engleski

Exploring Limit Behaviour of Non-quadratic Terms via H-measures. Application to Small Amplitude Homogenisation.

Original H-measures explore a quadratic limit behaviour of bounded ${; ; \rm L}; ; ^2$ sequences. We investigate possibilities of handling a general ${; ; \rm L}; ; ^p, p>2$ sequences and describing, roughly speaking, a microlocal limit of $\int|u_n|^p$ via (original) H-measures. The method 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 formulae for higher order correction terms. 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.

H-measures ; small amplitude homogenisation ; non-quadratic terms.

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