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Diffusion

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Part of the book series: UNITEXT ((UNITEXTMAT,volume 87))

Abstract

We shall recall a few notions and results that crop up frequently concerning the diffusion equation

$${u_t} - D\Delta u = f$$

defined on a cylindrical domain Q T = Ω × (0, T), where Ω is a domain (connected, open subset) of ℝn. Here u = u(x, t), and the Laplacian Δ is taken with respect to the spatial variables x only.

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© 2015 Springer International Publishing Switzerland

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Salsa, S., Verzini, G. (2015). Diffusion. In: Partial Differential Equations in Action. UNITEXT(), vol 87. Springer, Cham. https://doi.org/10.1007/978-3-319-15416-9_1

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