Foundation Sciences Faculty
Telecommunications University
101 Mai Xuan Thuong
Nha Trang, Khanh Hoa, Vietnam
email: dangthanhson@tcu.edu.vn, dangthanhson1810@gmail.com
Dang Thanh Son
Abstract:
In this article, we study the long time behavior of solutions to the 2D
magnetic Benard problem in porous media, considering on an arbitrary
(bounded or unbounded) domain satisfying Poincare inequality.
We first prove the existence of a weak solution and a global attractor
for the problem. For \(r=1,2,3\), we derive estimates for Hausdorff as well
as fractal dimensions of the global attractors. We then show an upper
semicontinuity of global attractors and final study the exponential
stability of a stationary solution to the problem.
Submitted December 2, 2024. Published March 20, 2025.
Math Subject Classifications: 35B40, 35B41, 35Q35, 37L30, 76W05.
Key Words: Magnetic Benard problem; global attractor; porus medium
fractal and Hausdroff dimensions; upper semicontinuity; stationary solution.
DOI: 10.58997/ejde.2025.30
Show me the PDF file (465 KB), TEX file for this article.
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Dang Thanh Son Foundation Sciences Faculty Telecommunications University 101 Mai Xuan Thuong Nha Trang, Khanh Hoa, Vietnam email: dangthanhson@tcu.edu.vn, dangthanhson1810@gmail.com |
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