Heat equation
Heat equation 28 languages Article Talk Read Edit View history From Wikipedia, the free encyclopedia Animated plot of the evolution of the temperature in a square metal plate as predicted by the heat equation. The height and redness indicate the temperature at each point. The initial state has a uniformly hot hoof-shaped region (red) surrounded by uniformly cold region (yellow). As time passes the heat diffuses into the cold region. In mathematics and physics , the heat equation is a certain partial differential equation . Solutions of the heat equation are sometimes known as caloric functions . The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. As the prototypical parabolic partial differential equation , the heat equation is among the most widely studied topics in pure mathematics , and ...