Homogenisation of parabolic/hyperbolic media
Provides theoretical and numerical tools for homogenisation of mixed-type evolutionary problems, but the contribution is incremental as it extends known techniques to a specific oscillatory setting.
The paper tackles homogenisation of media that rapidly oscillate between parabolic and hyperbolic states, proving convergence and presenting a numerical method with supporting numerical study.
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.