Pullback attractors for non-autonomous MGT-Fourier system
Year: 2024
Type: article
Abstract: In this paper, we consider the asymptotic behavior of solutions for the non-autonomous MGT-Fourier system$\left\{ \begin{array}{l}u_{ttt}+\alpha u_{tt}-\beta\Delta u_t-\gamma \Delta u+\eta\Delta\theta+f_1(u, u_t, \theta) = h_1(x, t), \\\theta_t-\kappa\Delta\theta-\eta\Delta u_{tt}-\eta\alpha\Delta u_t+f_2(u, u_t, \theta) = h_2(x, t). \end{array} \right.$We establish the existence of pullback attractors by proving the evolution process is pullback asymptotically compact and possesses a pullback absorbing family. Then, we study the upper semicontinuity of the pullback attractors as a non-autonomous perturbation tends to zero. We prove the family of pullback attractors converges to the corresponding compact global attractors associated with the autonomous limit problem when $ \varepsilon\rightarrow 0 $. Furthermore, we investigate the residual continuity of pullback attractors.
DOI: 10.3934/eect.2024069
Authors: Yang Wang, Jihui Wu
Institution: Shanghai University of Engineering Science
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405921745