03-370 Biryuk A.

Note on the transformation that reduces the Burgers equation to the heat equation. (16K, LATeX 2e) Aug 14, 03

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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.

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