The Cauchy- Problem With the Heat Equation
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Date
2014-06-06
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Addis Ababa University
Abstract
This report attempts to study solution of explicit linear PDE of second order, the heat equation
u k u f t
With certain symmetry condition on the solution u .In this regard, some sort of scaling of variables is
introduced and pertinent scaling transformation T that leaves the ratio
t
x
2
unchanged is shown to
usher to a solution of the form:
t
x
u x t v
2
,
Which is radial and hence a symmetric function.
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Keywords
Cauchy- Problem, Heat, Equation