The Heat Equation

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Other literature type 01 Jan 2016Publisher:Springer International Publishing

Authors: Hervé Le Dret; Brigitte Lucquin;

doi: 10.1007/978-3-319-27067-8_7

The Heat Equation

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Abstract

We have so far studied elliptic problems, i.e., stationary problems. We now turn to evolution problems, starting with the archetypal parabolic equation, namely the heat equation. In this chapter, we will present a brief and far from exhaustive theoretical study of the heat equation. We will mostly work in one dimension of space, some of the results having an immediate counterpart in higher dimensions, others not. The study of numerical approximations of the heat equation will be the subject of the next chapter.

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