Degtyarev S. Behaviour of interfaces in some mathematical models of filtration.

The thesis studies interfaces which are connected to evolution models for partial differential equations with the aim to establish sharp with respect to order estimates for the dimensions of the interfaces. For the first time such estimates are obtained in cases of the instantaneous support shrinking for a broad class of equations and in case of finite speed of propagation for parabolic equation with anisotropic degeneration. Methods of local integral estimates and the Newton method for solving nonlinear equations were used. The thesis has theoretical character and can be used for further theoretical investigations in the field of partial differential equations.