Homogenisation of parabolic/hyperbolic media

2018/10/02 by Sebastian Franz, Franz, Sebastian, Marcus Waurick +1
Computer Science · Engineering · #35B27 #35B35 #35M10 #65M12 #65M60 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1810.01234

openalex publication_date 2018/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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