Author: A. M. Vinogradov
In this note we announce some new results concerning second order
differential parabolic equation in two independent variables. It
turns out that any such equation is of Monge-Ampere type. These
latter are characterized by the fact that the associated
subsidiary equations describing singularities of their multivalued
solutions has, in a sense, the simplest form. The structure of
these subsidiary equations allows to subdivide parabolic equations
into four classes. Each of them can be described as a special
geometrical structure on 4-dimensional manifolds introduced below.
Beside other, this leads to a complete classification of
considered parabolic equations with respect to the group of
Our approach differs from the traditional one by the fact that we focus on the corresponding subsidiary, or characteristic, equations rather than on original ones. This leads to a noteworthy simplification.
Last revised November 25, 2008. 6 pages, LaTeX-2e.
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