Geodesic
Hyperbolic boundary layer in the vicinity of the shear wave front in shells of revolution
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 24 (2024) no. 3, pp. 394-401

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Hyperbolic boundary layer equations in thin shells of revolution are constructed in small vicinities of the shear wave fronts (taking into account its geometry) at edge shock loading of the normal type. Special coordinate system is used for defining the small boundary layer region. In this system, the coordinate lines defined by the normal to the middle surface are replaced by lines forming the surface of the shear wave front. The asymptotic model of the geometry of such a wave front suggests that these lines are formed by rotated normal to the middle surface. Asymptotically main components of considered stress strain state are defined: the normal displacement and the shear stress. The governing equation of this boundary layer is the hyperbolic equation of the second order with the variable coefficients for the normal displacement. 
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     author = {I. V. Kirillova},
     title = {Hyperbolic boundary layer in the vicinity of the shear wave front in shells of revolution},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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I. V. Kirillova. Hyperbolic boundary layer in the vicinity of the shear wave front in shells of revolution. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 24 (2024) no. 3, pp. 394-401. http://geodesic.mathdoc.fr/item/ISU_2024_24_3_a6/