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
- Complete basis | 150
- Computational physics | 111, 312, 8
- Fourier transform | 186, 321, 3
- Heat-dirichlet.1d.freefem | 21
- Heat-dirichlet-2d-freefem | 22
- History of the Fourier series | 17
- Important partial differential equation | 43, 793, 24
- Laplace's equation | 83, 188, 5
- Robin boundary condition | 117
- Separation of variables | 82
- Solving partial differential equations with the Fourier series | 74
- Time-independent Schrodinger equation | 381
- Wave equation | 124, 418, 16