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Asymptotic dynamic of the nonclassical diffusion equation with time-dependent coefficient
Jing Wang,Qiaozheng 马巧珍 Ma
Keywords:Nonclassical diffusion equation, Time-dependent 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 time-dependent space $\mathcal{H}_{t}$ with the norm depending on time $t$ explicitly. Then we establish the existence, regularity and asymptotic structure of the time-dependent global attractor.