- 03-370 Biryuk A.
- Note on the transformation that reduces the Burgers equation to
the heat equation.
(16K, LATeX 2e)
Aug 14, 03
(auto. generated ps),
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Abstract. While trying to trace the history of the Burgers equation we
found a few forgotten (or at least not very well known)
facts about/related to it.
The first is the Forsyth's theorem about
the possibility of making a linear transformation
of a linear parabolic equation to the heat equation.
The second is that
in the late forties Florin used the 3D Burgers equation to study
wet soil and as a tool developed the reduction to the heat equation.
The third is
a uniqueness theorem for the Burgers equation
(without growth restrictions),
which is equivalent to the Widder uniqueness theorem
for the heat equation in the class of positive solutions.