Biryuk A.
Note on the transformation that reduces the Burgers equation to
the heat equation.
(16K, LATeX 2e)
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.