On some initial-boundary-value problems in aerohydroelasticity

In this problem, we consider problems of the dynamics and stability of deformable structural elements interacting with a fluid or gas flow. Mathematical models considered are initial-boundary-value problems for coupled systems of partial differential equations for hydrodynamic functions and deformation functions of elastic elements. To study the dynamics and stability of deformable elements interacting with an ideal medium, we use various methods of the theory of functions of complex variables, the Fourier method, the Bubnov–Galerkin method, and the method of Lyapunov functionals.