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arXiv · 1801.01918

Homogenization of some degenerate pseudoparabolic variational inequalities

Mariya Ptashnyk
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Abstract

Multiscale analysis of a degenerate pseudoparabolic variational inequality, modelling the two-phase flow with dynamical capillary pressure in a perforated domain, is the main topic of this work. Regularisation and penalty operator methods are applied to show the existence of a solution of the nonlinear degenerate pseudoparabolic variational inequality defined in a domain with microscopic perforations, as well as to derive a priori estimates for solutions of the microscopic problem. The main challenge is the derivation of a priori estimates for solutions of the variational inequality, uniformly with respect to the regularisation parameter and to the small parameter defining the scale of the microstructure. The method of two-scale convergence is used to derive the corresponding macroscopic obstacle problem.

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Mariya Ptashnyk. 2018-01-05. Homogenization of some degenerate pseudoparabolic variational inequalities. https://doi.org/10.1016/j.jmaa.2018.08.047

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