Non-autonomous perturbations of a non-classical non-autonomous parabolic equation with subcritical nonlinearity

Abstract

Abstract In this work we study the continuity of four different notions of asymptotic behavior for a family of non-autonomous non-classical parabolic equations given by { u t − γ ( t ) Δ u t − Δ u = g ϵ ( t , u ) , in Ω u = 0 , on ∂ Ω . $$\begin{array}{} \displaystyle \left\{ \begin{array}{*{20}{l}} {{u_t} - \gamma \left( t \right)\Delta {u_t} - \Delta u = {g_\varepsilon }\left( {t,u} \right),{\;\text{in}\;}\Omega } \hfill \\ {u = 0,{\;\text{on}\;}\partial \Omega {\rm{.}}} \hfill \\ \end{array}\right. \end{array}$$ in a smooth bounded domain Ω ⊂ ℝ n , n ⩾ 3, where the terms g ε are a small perturbation, in some sense, of a function f that depends only on u .