3. A parabolic equation: the heat equation

3.1 Heat equation in dimension 1

It is the following partial differential equation: $\frac{\partial u}{\partial t} = \frac{γ}{c} \frac{\partial^{2} u}{\partial x^{2}} .$

The constants c and γ denote the thermal capacity and conductivity of a bar, and u (x, t ) indicates the temperature at the bar's x-axis point at time t.

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References

(1) - REINHARD (H.) - Équations différentielles - , Gauthier-Villars.
(2) - REINHARD (H.) - Équations aux dérivées partielles - , Dunod.
(3) - YOSIDA (K.) - Équations différentielles...

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