### 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.

Language | English |
---|---|

Pages | 44-75 |

Number of pages | 32 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 469 |

Issue number | 1 |

Early online date | 28 Aug 2018 |

DOIs | |

State | Published - 1 Jan 2019 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

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*Journal of Mathematical Analysis and Applications*, vol. 469, no. 1, pp. 44-75. DOI: 10.1016/j.jmaa.2018.08.047

**Homogenization of some degenerate pseudoparabolic variational inequalities.** / Ptashnyk, Mariya.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Homogenization of some degenerate pseudoparabolic variational inequalities

AU - Ptashnyk,Mariya

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Degenerate nonlinear PDEs

KW - Homogenization

KW - Obstacle problems

KW - Penalty operator method

KW - Pseudoparabolic inequalities

KW - Two-scale convergence

UR - http://www.scopus.com/inward/record.url?scp=85053145398&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2018.08.047

DO - 10.1016/j.jmaa.2018.08.047

M3 - Article

VL - 469

SP - 44

EP - 75

JO - Journal of Mathematical Analysis and Applications

T2 - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -