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On the solvability of steady-state transonic equations in an unbounded domain. (English. Russian original) Zbl 0762.76049
Math. USSR, Sb. 70, No. 1, 31-45 (1991); translation from Mat. Sb. 181, No. 5, 610-624 (1990).
The author studies the equation \(u_ xu_{xx}-\Delta_ yu+\alpha u_ x=0\), where \((x,y)\in {\mathbb{R}}\times \Omega\), \(\Omega\subset {\mathbb{R}}^ 3\), with nonzero Neumann boundary condition on \({\mathbb{R}}\times \partial \Omega\). He proves existence of a viscosity solution for this nonlinear boundary value problem of mixed elliptic-hyperbolic-parabolic type and shows that this solution is classical. The problem models a steady-state transonic flow of a chemical mixture in a cylinder. In the translation from the Russian original \(\Delta\) has been replaced randomly with \(\triangledown\).
Reviewer: G.H.Sweers (Delft)

MSC:
76H05 Transonic flows
35Q35 PDEs in connection with fluid mechanics
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