Homogenization of some degenerate pseudoparabolic variational inequalities

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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.

Original languageEnglish
Pages (from-to)44-75
Number of pages32
JournalJournal of Mathematical Analysis and Applications
Volume469
Issue number1
Early online date28 Aug 2018
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Degenerate nonlinear PDEs
  • Homogenization
  • Obstacle problems
  • Penalty operator method
  • Pseudoparabolic inequalities
  • Two-scale convergence

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