Conference paper
A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem

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Author list: Jonasson, Pernilla
Publisher: American Institute of Physics (AIP)
Publication year: 2017
ISBN: 9780735414648
View additional information: View in Web of Science™

Abstract

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 ??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 ?-1?tu? 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.


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