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Fundam. Prikl. Mat., 1999, Volume 5, Issue 4, Pages 1179–1189 (Mi fpm443)  

Formally integrable Mizohata systems of codimension 1

I. B. Tabov

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Abstract: In the paper we prove that any formally integrable Mizohata system of codimension one
$$\{
\begin{array}{@ l@ } \partial_1u=\epsilon_1ix^1\partial_nu+f_1,
\partial_2u=\epsilon_2ix^2\partial_nu+f_2,
………
\partial_{n-1}u=\epsilon_{n-1}ix^{n-1}\partial_nu+f_{n-1} \end{array}
. $$
can be reduced by a local change of the variables to a system of the form
$$\{
\begin{array}{@ l@ } \partial_1v^1+\partial_2v^2=\psi _1,
\partial_1v^2-\partial_2v^1=\psi _2 \end{array}
. $$
and, consequently, to Poisson's equation in the plane.

Full text: PDF file (388 kB)

Bibliographic databases:
UDC: 517.956
Received: 01.04.1996

Citation: I. B. Tabov, “Formally integrable Mizohata systems of codimension 1”, Fundam. Prikl. Mat., 5:4 (1999), 1179–1189

Citation in format AMSBIB
\Bibitem{Tab99}
\by I.~B.~Tabov
\paper Formally integrable Mizohata systems of codimension~1
\jour Fundam. Prikl. Mat.
\yr 1999
\vol 5
\issue 4
\pages 1179--1189
\mathnet{http://mi.mathnet.ru/fpm443}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1782960}
\zmath{https://zbmath.org/?q=an:0959.35032}


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