Abstract
<abstract><p>In this paper, we consider the long-time dynamical behavior of the MGT-Fourier system</p>
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$\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) = 0,\nonumber\\ \theta_t-\kappa\Delta\theta-\eta\Delta u_{tt}-\eta\alpha\Delta u_t+f_2(u,u_t,\theta) = 0.\nonumber \end{array}} \right. $
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<p>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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
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