6. Transient problems

6.1 Heat equation

We give ourselves a bounded open Ω of R ⁿ , boundary Γ, the unknown u (x, t) is the temperature, whose evolution we study given an initial condition u ₀ and a boundary condition that we assume to be zero for simplicity, i.e. :

\begin{array}{l} \frac{\partial u}{\partial t} - Δ u = f dans Ω \times] 0, \end{array}

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Bibliography

References

(1) - BREZIS (H.) - Analyse fonctionnelle - Masson (1983).
(2) - ARVESON (W.) - A Short Course on Spectral Theory - Springer-Verlag (2002).
(3)...

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