# Heat equation

partial differential equation for distribution of heat in a given region over time

The heat equation is a type of equation used in mathematics and physics to describe how heat spreads out in a particular area. The equation was first created by Joseph Fourier in 1822. People use the heat equation to model how heat spreads through different materials.

The heat equation is very important in the field of mathematics, and it is studied a lot. This equation is used in many areas of science and applied mathematics, such as probability theory and image analysis. Some solutions to the heat equation are called heat kernels, and they can provide important information about the area where the heat is spreading.

Scientists have found many different ways to use the heat equation. For example, it can be used to study random walks and Brownian motion in probability theory, and it can help to resolve pixelation in image analysis. In addition, variants of the heat equation are used in financial mathematics and quantum mechanics. Scientists have also found that solutions of the heat equation are helpful in understanding hydrodynamical shocks. People have been studying the heat equation for a long time, and it is a very important topic in mathematics and physics.