Geodesic
Application in aerohydrodynamics of the solution of an inverse boundary value problem for analytic functions
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 1, pp. 80-89

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We consider a modified inverse boundary value problem of aerohydrodynamics in which it is required to find the shape of an airfoil streamlined by a potential flow of an incompressible nonviscous fluid, when the distribution of the velocity potential on one section of the airfoil is given as a function of the abscissa, while, on other sections of the airfoil, as a function of the ordinate of the point. The velocity of the undisturbed flow streamlining the sought-for airfoil is determined in the process of solving the problem. It is shown that, under rather general conditions on the initially set functions, the sought-for contour is closed unlike the inverse problem in the case when, on the unknown contour, the velocity distribution is given as a function of the arc abscissa of the contour point. We also consider the case when, on the entire desired contour, the distribution of the velocity potential is given as a function of one and the same Cartesian coordinate of the contour point.
Keywords: inverse boundary value problems of aerodynamics, analytic function, conformal mapping
Mots-clés : airfoil. 
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     author = {R. B. Salimov},
     title = {Application in aerohydrodynamics of the solution of an inverse boundary value problem for analytic functions},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {80--89},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2018_21_1_a7/}
}
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R. B. Salimov. Application in aerohydrodynamics of the solution of an inverse boundary value problem for analytic functions. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 1, pp. 80-89. http://geodesic.mathdoc.fr/item/SJIM_2018_21_1_a7/