Rodríguez Bernal, AníbalVidal López, AlejandroRobinson, James C.2023-06-202023-06-2020070022-039610.1016/j.jde.2007.03.028https://hdl.handle.net/20.500.14352/49691We analyse the dynamics of the non-autonomous nonlinear reaction–diffusion equation ut −_u = f (t,x,u), subject to appropriate boundary conditions, proving the existence of two bounding complete trajectories, one maximal and one minimal. Our main assumption is that the nonlinear term satisfies a bound of the form f (t,x,u)u _ C(t, x)|u|2 + D(t, x)|u|, where the linear evolution operator associated with _ + C(t, x) is exponentially stable. As an important step in our argument we give a detailed analysis of the exponential stability properties of the evolution operator for the non-autonomous linear problem ut − _u = C(t, x)u between different Lp spaces.engjournal articlehttp://www.sciencedirect.com/science/journal/00220396open access517.9517.938Pullback attractorsExtremal complete trajectoriesReaction-diffusion equationEvolution operatorExponentially stableNon-autonomous logistic equationEcuaciones diferenciales1202.07 Ecuaciones en Diferencias