Besides being useful in engineering, it was very important historically from a "development of mathematics point of view", e.g. it was the initial motivation for the Fourier series.
Some interesting properties:
- TODO confirm: for a fixed boundary condition that does not depend on time, the solutions always approaches one specific equilibrium function.This is in contrast notably with the wave equation, which can oscillate forever.
- TODO: for a given point, can the temperature go down and then up, or is it always monotonic with time?
- information propagates instantly to infinitely far. Again in contrast to the wave equation, where information propagates at wave speed.
- The best articles by Ciro Santilli | 2k
- Computational physics | 109, 290, 8
- Heat-dirichlet.1d.freefem | 19
- Heat-dirichlet-2d-freefem | 20
- History of the Fourier series | 17
- Important partial differential equation | 43, 608, 21
- Laplace's equation | 83, 140, 4
- Robin boundary condition | 113
- Solving partial differential equations with the Fourier series | 72