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\begin{document}

\title{Asymptotic behavior of the Boussinesq equation with nonlocal weak
damping and arbitrary growth nonlinear function}



\author[1]{Yichun Mo}%
\author[1]{Qiaozhen Ma}%
\author[1]{Lijuan YAO}%
\affil[1]{Northwest Normal University}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\begin{abstract}
In this paper, we consider the asymptotic behavior of the Boussinesq
equation with nonlocal weak damping when the nonlinear function is
arbitrary polynomial growth. We firstly prove the well-posedness of
solution by means of the monotone operator theory. At the same time, we
obtain the dissipative property of the dynamical system (E \emph{,S}(
\emph{t})) associated with the problem in the space H 0 2 (  ) \selectlanguage{ngerman}× L 2 (
\selectlanguage{english} ) and D ( A 3 4 ) x H 0 1 ( \selectlanguage{english} ) , respectively. After that, the
asymptotic smoothness of the dynamical system (E \emph{,S}( \emph{t}))
and the further quasi-stability are demonstrated by the energy
reconstruction method. Finally, different from {[}21{]} we show not only
existence of the finite global attractor but also existence of the
generalized exponential attractor.%
\end{abstract}\selectlanguage{ngerman}%



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