On pullback attractors in non-autonomous dynamical systems

The theory of pullback attractors constitutes an important tool to interpret the dynamics of physical, biological or engineering phenomena, as it addresses the study of the asymptotic behavior of nonautonomous dynamic systems, where differential equations explicitly depend on time. The objective of this article seeks to synthesize recent advances, present some general techniques such as the energy estimations or asymptotic compactness. This work stick out the importance of pullback attractors to model systems with variable coefficients, memory, delays or in non-cylindrical domains and also points out some challenges such as extension to stochastic systems or complex geometries.