Asymptotic dynamic of the nonclassical diffusion equation with timedependent coefficient 
Jing Wang,Qiaozheng Ma 
Keywords:Nonclassical diffusion equation，timedependent global attractor，polynomial growth of arbitrary order，asymptotic structure,regularity. 
Abstract: 
We study the asymptotic behavior of solutions for a nonclassical diffusion equation with polynomial growth condition of arbitrary order $p\geq2$ on bounded domain~$\Omega\subset\mathbb{R}^{N}$~with smooth boundary~$\partial\Omega$. Firstly, the existence and uniqueness of weak solution are obtained in the timedependent space $\mathcal{H}_{t}$ with the norm depending on time $t$ explicitly. Then we establish the existence, regularity and asymptotic structure of the timedependent global attractor. 



