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Article | REF: AF190 V1

Partial differential equations

Authors: Claude BARDOS, Thierry PAUL

Publication date: October 10, 2010

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5. Heat equation

5.1 Context

The heat propagation equation appears in Fourier's memoir. Of course, at the time, there was no explanation of heat derived from atomic theory (as there is now, from the Boltzmann equation). On the other hand, we had a good notion of the propagation of this object, saying that propagation was proportional to the variation in the temperature gradient. A balance equation then gives in a domain Ω with κ the heat conductivity.

∂t u−∇(κ ∇u)=g
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