Abstract
This survey provides a concise yet comprehensive overview on enhanced dissipation phenomena, transitioning seamlessly from the physical principles underlying the interplay between advection and diffusion to their rigorous mathematical formulation and analysis. The discussion begins with the standard theory of enhanced dissipation, highlighting key mechanisms and results, and progresses to its applications in notable nonlinear PDEs such as the Cahn-Hilliard and the Kuramoto-Sivashinsky equations.
•This survey provides a concise yet comprehensive overview on enhanced dissipation.•Applications to non-linear PDEs are discussed.•Taylor's dispersion is compared to enhanced dissipation.•Hypocoercivity methods are reviewed.•Resolvent estimates are presented.