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Time dependent perturbation in a non-autonomous non-classical parabolic equation

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  • n this paper we study the existence and characterization of a pullback attractor for a non-autonomous non-classical parabolic equation of the form \begin{equation}\label{EQnoncla} \left\{ \begin{split} &u_t-\gamma(t)\Delta u_t-\Delta u=f(u) \mbox{ in }\Omega,\\ &u=0 \mbox{ on }\partial\Omega \end{split} \right. (1) \end{equation} in a sufficiently smooth bounded domain $\Omega\subset\mathbb R^n$ with $f$ and $\gamma$ satisfying some suitable natural conditions. We prove the well posedness of this model and the existence of a pullback attractor. We show that this pullback attractor is characterized as the union of unstable sets of the associated equilibria and that this characterization is stable under time dependent perturbation of the nonlinearity.
    Mathematics Subject Classification: 35B20, 35B50, 35K55, 37B55, 37C70.


    \begin{equation} \\ \end{equation}
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