# Seminars

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# Colloquium: G-convergence and homogenization of two-phase flows

2007-09-13

4:10 p.m. Neill Hall 5W

Alexander Panchenko

We study the system of balance equations modeling the flow of a two-phase, Kelvin-Voight viscoelastic material. We consider a sequence of highly oscillatory initial data, parametrized by a small parameter. The initial geometry is generic in the sense that periodicity or even random homogeneity are not assumed. Using G-convergence and oscillating test functions, we pass to the limit and obtain an effective system of equations. These equations model a one-phase viscoelastic flow. The mass balance equation and convective terms in the momentum balance equation have the standard structure. The constitutive equation for effective stress contains a long memory term which is not present in the -problems.