A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem
2017 (English)In: AIP Conference Proceedings, American Institute of Physics (AIP), 2017, Vol. 1798, 020177Conference paper (Refereed)
We study the homogenization of a hyperbolic-parabolic PDE with oscillations in one fast spatial scale. Moreover, the first order time derivative has a degenerate coefficient passing to infinity when ϵ→0. We obtain a local problem which is of elliptic type, while the homogenized problem is also in some sense an elliptic problem but with the limit for ϵ-1∂tuϵ as an undetermined extra source term in the right-hand side. The results are somewhat surprising and work remains to obtain a fully rigorous treatment. Hence the last section is devoted to a discussion of the reasonability of our conjecture including numerical experiments.
Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2017. Vol. 1798, 020177
IdentifiersURN: urn:nbn:se:miun:diva-30455DOI: 10.1063/1.4972769ScopusID: 2-s2.0-85013657168ISBN: 978-073-5414-64-8 (print)OAI: oai:DiVA.org:miun-30455DiVA: diva2:1081147
11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, 4 July 2016 through 8 July 2016, University of La Rochelle La Rochelle; France