IJPAM: Volume 97, No. 3 (2014)

ON UNIQUENESS MORAWETZ PROBLEM
FOR THE CHAPLYGIN EQUATION

Andrey Anatolievicn Akimov
Bashkir State University
Sterlitamak Branch
453103, Lenina Street, 47A, Sterlitamak, RUSSIA


Abstract. For the equation

\begin{displaymath}Lz=K(y)z_{xx} +z_{yy} =0,\end{displaymath}

where $yK(y)>0$ for $y\ne 0$) in $D$, bounded by a Jordan (non-selfintersecting) "elliptic" arc $\Gamma $ (for $>$ 0) with endpoints $A(0,0)$and $B(l,0),\; l>0$, and for $y<0$ by a characteristic $\gamma _{1} $ through A which meets the characteristic $\gamma _{2} $ through B at the points C, the uniqueness of the Morawetz problem is proved without assuming that $\Gamma $ is monotone.

Received: September 14, 2014

AMS Subject Classification: 35M12

Key Words and Phrases: Chaplygin equation, Morawetz problem, equation of mixed type

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DOI: 10.12732/ijpam.v97i3.9 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 3
Pages: 369 - 375


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