Homogenisation of parabolic/hyperbolic media

Abstract

We consider an evolutionary problem with rapidly oscillating coefficients. This causes the problem to change frequently between a parabolic and an hyperbolic state. We prove convergence of the homogenisation process in the unit square and present a numerical method to deal with approximations of the resulting equations. A numerical study finalises the contribution.

Submitted to the Proceedings of BAIL 2018; 12 pages