$L^{p}$-pullback attractors for non-autonomous reaction-diffusion equations with delays

Kaixuan Zhu, Yongqin Xie, Feng Zhou

DOI: http://dx.doi.org/10.12775/TMNA.2019.020

Abstract


In this paper, we consider the non-autonomous reaction-diffusion equations with hereditary effects and the nonlinear term $f$ satisfying the polynomial growth of arbitrary order $p-1$ $(p\geq2)$. The delay term may be driven by a function with very weak assumptions, namely, just measurability. We extend the asymptotic \emph{a priori} estimate method (see \cite{ZYS06}) to our problem and establish a new existence theorem for the pullback attractors in $C_{L^{p}(\Omega)}$ $(p> 2)$ (see Theorem \ref{t2.5}), which generalizes the results obtained in \cite{GM14}.

Keywords


Reaction-diffusion equations; delays; pullback attractors

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