Parabolic equations are a type of second-order partial differential equation that describe various phenomena in physics and engineering. They are characterized by their parabolic shape when graphed, resembling a "U" or an inverted "U." A common example is the heat equation, which models how heat diffuses through a material over time. These equations often arise in problems involving time-dependent processes, such as heat transfer or diffusion. The solutions to parabolic equations typically involve initial and boundary conditions, which help determine the behavior of the system being studied. Understanding these equations is essential for fields like mathematics, physics, and engineering.