Questions tagged [heat-equation]

The heat equation is a particular parabolic partial differential equation used to describe the temperature or heat distribution of a system over time. It can be written most generally as

$$\frac{\partial u}{\partial t} - \alpha \nabla^2 u = 0$$

where $\nabla^2$ is the Laplace operator, and $\alpha$ is a positive constant describing thermal diffusivity (which is usually normalized to $1$).

There are a number of common solution techniques, including separation of variables and Fourier series, as well as using a Green's function to find a fundamental solution.

Reference: Heat equation.