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The heat equation is an important partial differential equation which describes the distribution of heat in a given region over time. For a function u of three spatial variables and the time variable t, the heat equation is where is a constant. The heat equation is of fundamental importance in diverse scientific fields. In mathematics, it is the prototypical parabolic partial differential equation. In probability theory, the heat equation is connected with the study of Brownian motion via the Fokker Planck equation. The diffusion equation, a more general version of the heat equation, arises in connection with the study of chemical diffusion and other related processes.