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Volume 14, Issue 1
Analysis of a System of Hemivariational Inequalities Arising in Non-Stationary Stokes Equation with Thermal Effects

Hailing Xuan & Xiaoliang Cheng

DOI: 10.4208/eajam.2022-353.260523

East Asian J. Appl. Math., 14 (2024), pp. 124-146.

Published online: 2024-01

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  • Abstract

A non-stationary Stokes equation coupled with an evolution equation of temperature field is studied. Boundary conditions for velocity and temperature fields contain the generalized Clarke gradient. The corresponding variational formulation is governed by a system of hemivariational inequalities. The existence and uniqueness of a weak solution is proved by employing Banach fixed point theorem and hemivariational inequalities. Besides, a fully-discrete problem for this system of hemivariational inequalities is given and error estimates are derived.

  • Keywords

Non-stationary Stokes equation, hemivariational inequality, thermal effects, Banach fixed point theorem, numerical analysis.

  • AMS Subject Headings

65M15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-14-124, author = {Xuan , Hailing and Cheng , Xiaoliang}, title = {Analysis of a System of Hemivariational Inequalities Arising in Non-Stationary Stokes Equation with Thermal Effects}, journal = {East Asian Journal on Applied Mathematics}, year = {2024}, volume = {14}, number = {1}, pages = {124--146}, abstract = {

A non-stationary Stokes equation coupled with an evolution equation of temperature field is studied. Boundary conditions for velocity and temperature fields contain the generalized Clarke gradient. The corresponding variational formulation is governed by a system of hemivariational inequalities. The existence and uniqueness of a weak solution is proved by employing Banach fixed point theorem and hemivariational inequalities. Besides, a fully-discrete problem for this system of hemivariational inequalities is given and error estimates are derived.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2022-353.260523}, url = {http://global-sci.org/intro/article_detail/eajam/22322.html} }
TY - JOUR T1 - Analysis of a System of Hemivariational Inequalities Arising in Non-Stationary Stokes Equation with Thermal Effects AU - Xuan , Hailing AU - Cheng , Xiaoliang JO - East Asian Journal on Applied Mathematics VL - 1 SP - 124 EP - 146 PY - 2024 DA - 2024/01 SN - 14 DO - http://doi.org/10.4208/eajam.2022-353.260523 UR - https://global-sci.org/intro/article_detail/eajam/22322.html KW - Non-stationary Stokes equation, hemivariational inequality, thermal effects, Banach fixed point theorem, numerical analysis. AB -

A non-stationary Stokes equation coupled with an evolution equation of temperature field is studied. Boundary conditions for velocity and temperature fields contain the generalized Clarke gradient. The corresponding variational formulation is governed by a system of hemivariational inequalities. The existence and uniqueness of a weak solution is proved by employing Banach fixed point theorem and hemivariational inequalities. Besides, a fully-discrete problem for this system of hemivariational inequalities is given and error estimates are derived.

Xuan , Hailing and Cheng , Xiaoliang. (2024). Analysis of a System of Hemivariational Inequalities Arising in Non-Stationary Stokes Equation with Thermal Effects. East Asian Journal on Applied Mathematics. 14 (1). 124-146. doi:10.4208/eajam.2022-353.260523
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