Attractors for a class of perturbed nonclassical diffusion equations with memory

Abstract

<p style='text-indent:20px;'>In this paper, using a new operator decomposition method (or framework), we establish the existence, regularity and upper semi-continuity of global attractors for a perturbed nonclassical diffusion equation with fading memory. It is worth noting that we get the same conclusion in [<xref ref-type="bibr" rid="b7">7</xref>,<xref ref-type="bibr" rid="b14">14</xref>] as the perturbed parameters <inline-formula><tex-math id="M1">\begin{document}$ \nu = 0 $\end{document}</tex-math></inline-formula>, but the nonlinearity <inline-formula><tex-math id="M2">\begin{document}$ f $\end{document}</tex-math></inline-formula> satisfies arbitrary polynomial growth condition rather than critical exponential growth condition.</p>