Uniform attractors for nonautonomous MGT‐Fourier system.

In this paper, we consider the dynamical behavior of nonautonomous MGT‐Fourier system uttt+αutt−βΔut−γΔu+ηΔθ=f(x,t),θt−κΔθ−ηΔutt−ηαΔut=g(x,t),$$ \left\{\begin{array}{l}{u}_{tt t}+\alpha {u}_{tt}-\beta \Delta {u}_t-\gamma \Delta u+\eta \Delta \theta =f\left(x,t\right),\\ {}{\theta}_t-\kappa \Delta \theta -\eta \Delta {u}_{tt}-\eta \alpha \Delta {u}_t=g\left(x,t\right),\end{array}\right. $$We first establish the global existence and asymptotic behavior by semigroup method and multiplicative method. Next, we get the existence of the uniform attractors by the method of uniform contractive functions, which only need to verify compactness condition with the same type of energy estimates for establishing absorbing set. Finally, we also consider the semilinear case by semigroup method. [ABSTRACT FROM AUTHOR]