Homogenization of some degenerate pseudoparabolic variational inequalities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:469

Article

Ptashnyk, Mariya^1,2 

[1] Heriot Watt Univ, Sch Math & Comp Sci, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

[2] Univ Dundee, Div Math, Dundee DD1 4HN, Scotland

关键词: Pseudoparabolic inequalities;    Obstacle problems;    Degenerate nonlinear PDEs;    Homogenization;    Two-scale convergence;    Penalty operator method;   

DOI  :  10.1016/j.jmaa.2018.08.047

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free