Sanikidze T. Qualitative properties of solutions of non-stationary systems in the theory of magnetism

The thesis is devoted to the investigation of nonlinear non-stationary systems, which are considered as an approximation to well-known three-dimensional Bean's model of superconductivity II, systems with convection and systems of porous medium equations as well. The finite speed of propagation for all these systems were proven. The diapason of stability and non-stability for the tangent fracture to small perturbations in the form of the surface wave in a plane problem of magneto-oscillation stability was estimated. The exact solution for the system, which describes the degenerate magneto-acoustic wave propagation in the inhomogeneous magnetic field, was obtained.