Abstract
The simplest parabolic differential equation is (6.3) or, as we normally meet it, (6.3a):
in which u is given as a function of a space variable x and of time t, and in which the coefficient a is a constant. Strictly, this is a two-dimensional equation: u is a function of two co-ordinates. However, in the form, for example, of (7.2) below, this is usually called the ‘one-dimensional heat conduction equation’ because it describes the unsteady conduction of heat in one space dimension.
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© 1986 G. de Vahl Davis
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de Vahl Davis, G. (1986). Partial differential equations II — parabolic equations. In: Numerical Methods in Engineering & Science. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-6958-5_7
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DOI: https://doi.org/10.1007/978-94-011-6958-5_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-412-43880-6
Online ISBN: 978-94-011-6958-5
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