How does the heat equation change in the real world?

[lavinia]

The heat equation predicts that heat spreads infinitely far over arbitrarily small time intervals. What happens in real life? How does the heat equation get modified?

 

[espen180]

In the real (classical) world, you have to take into account relativity, which can be done by a well defined way of "upgrading" a Galileo-invariant equation to a corresponding Lorentz-invariant one. There is a relevant Wikipedia article you can read here: http://en.wikipedia.org/wiki/Relativistic_heat_conduction