@article{Wang2024, 
author = {Yang Wang and Jihui Wu},
title = {Long-time dynamics of nonlinear MGT-Fourier system},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {9152-9163},
keywords = {MGT-Fourier, well-posedness, global attractors, exponential attractors},
url = {https://www.sciopen.com/article/10.3934/math.2024445},
doi = {10.3934/math.2024445},
abstract = {In this paper, we consider the long-time dynamical behavior of the MGT-Fourier system               {                                                      u                              t                t                t                                      +            α                          u                              t                t                                      −            β            Δ                          u              t                        −            γ            Δ            u            +            η            Δ            θ            +                          f              1                        (            u            ,                          u              t                        ,            θ            )            =            0            ,                                                              θ              t                        −            κ            Δ            θ            −            η            Δ                          u                              t                t                                      −            η            α            Δ                          u              t                        +                          f              2                        (            u            ,                          u              t                        ,            θ            )            =            0.                                  First we use the nonlinear semigroup theory to prove the well-posedness of the solutions. Then we establish the existence of smooth finite dimensional global attractors in the system by showing that the solution semigroup is gradient and quasi-stable. Furthermore, we investigate the existence of generalized exponential attractors.}
}