Asymptotic methods for solving boundary value problems for symmetric and antisymmetric hyperbolic boundary layer in shells of revolution in the vicinity of dilatational and shear wave fronts

Asymptotic methods for solving boundary value problems for three types of hyperbolic boundary layers in the case of shells of revolution of arbitrary profile are developed: symmetric and antisymmetric boundary layers in the vicinity of the dilatation wave front and antisymmetric boundary layers in the vicinity of the shear wave front. The solutions are based on the use of solutions for the hyperbolic boundary layer in the case of a cylindrical shell, that is, on the so-called "basic solutions". The basic solutions are obtained using integral Laplace transforms with respect to time and Fourier transforms with respect to the longitudinal coordinate, followed by expansion of the Laplace images into a series of oscillation modes. Solutions for the general case of shells of revolution also use decompositions of the images into a series of oscillation modes, which are obtained using the exponential representation method. The obtained analytical solution methods fully implement