Geodesic
On solvability of stationary transonic equations in the unbounded domain
Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 31-45 Cet article a éte moissonné depuis la source Math-Net.Ru

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Solvability of a boundary value problem in an infinite cylinder is proved for an equation modelling steady-state transonic flows of a chemical mixture: \begin{gather} u_xu_{xx}-\nabla_yu+\alpha u_x=0, \\ \frac{\partial u}{\partial N}\bigg|_{\partial\Omega\times R^1}=\varphi(x,y),\quad \lim_{|x|\to\infty}u_x=0,\quad \lim_{x\to\infty}|\nabla_yu|=0, \end{gather} Where $y\in\Omega\subset R^2$, $x\in R^1$, and $\alpha$ is a positive parameter. Conditions on $\varphi (x,y)$ are established under which there exists a classical solution of problem (1), (2) which is unique up to an additive constant. 
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     title = {On~solvability of stationary transonic equations in the unbounded domain},
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     url = {http://geodesic.mathdoc.fr/item/SM_1991_70_1_a2/}
}
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N. A. Lar'kin. On solvability of stationary transonic equations in the unbounded domain. Sbornik. Mathematics, Tome 70 (1991) no. 1, pp. 31-45. http://geodesic.mathdoc.fr/item/SM_1991_70_1_a2/

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