Homogenization of some degenerate pseudoparabolic variational inequalities
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.
Keywords
Cite
@article{arxiv.1801.01918,
title = {Homogenization of some degenerate pseudoparabolic variational inequalities},
author = {Mariya Ptashnyk},
journal= {arXiv preprint arXiv:1801.01918},
year = {2018}
}