A discussion of a homogenization procedure for a degenerate linear hyperbolic-parabolic problem
Liselott Flodén, Anders Holmbom, Pernilla Jonasson, Tatiana Lobkova, Marianne Olsson Lindberg, Y. Zhang · AIP conference proceedings · 2017
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.