Homogenization of some degenerate pseudoparabolic variational inequalities |
| |
Institution: | 1. Department of Mathematics, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK;2. Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UK |
| |
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: | Pseudoparabolic inequalities Obstacle problems Degenerate nonlinear PDEs Homogenization Two-scale convergence Penalty operator method |
本文献已被 ScienceDirect 等数据库收录! |
|