FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1999, VOLUME 5, NUMBER 4, PAGES 1179-1189
J. Tabov
Abstract
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In the paper we prove that
any formally integrable Mizohata system
of codimension one
$$
\left \{
\begin{array}{@{}l@{}}
\partial _1u=\varepsilon_1ix^1\partial _nu+f_1, \\
\partial _2u=\varepsilon_2ix^2\partial _nu+f_2, \\
\dotfill \\
\partial _{n-1}u=\varepsilon_ {n-1}ix^{n-1}\partial _nu+f_{n-1}
\end{array}
\right.
$$
can be reduced by a local change of the variables to a system of the form
$$
\left \{
\begin{array}{@{}l@{}}
\partial _1 v^1 +\partial _2v^2=\psi _1, \\
\partial _1v^2 - \partial _2v^1=\psi _2
\end{array}
\right.
$$
and, consequently, to Poisson's equation in the plane.
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Last modified: December 9, 1999