On March 30 several Candidate of Science dissertations were defended at the Dissertation Council D 003.054.04 at Lavrentev Institute of Hydrodynamics SB RAS.
- Irina V. Fankina defended her dissertation "Boundary value problems on the equilibrium of two-layer structures with inclusions and cracks"
- Alexey I. Furtsev defended his dissertation "Boundary value problems on the contact of elastic plates and thin obstacles with one-sided constraints"
Both dissertations were carried out under the scientific supervision of Doctor of Physics and Mathematics, Professor Alexander M. Khludnev
, specialty 01.01.02 — Differential Equations, Dynamical Systems and Optimal Control.
Many structures encountered in practice consist of elastic bodies, plates and beams connected to each other. Cracks can occur in structures during construction or use. The presence of cracks in the structure can significantly reduce the indicators of the mechanical properties of the product. Therefore, the study of mathematical models describing the deformation of cracked structures is an urgent problem. I. V. Fankin's dissertation is devoted to the study of the properties of solutions of nonlinear boundary value problems describing the equilibrium of two-layer structures with cracks and defects.
A. I. Furtsev's dissertation is devoted to the study of boundary value problems on the contact of elastic plates and thin obstacles with one-sided constraints. These are problems describing elastic plates and obstacles that, when bent, can contact each other along a line. The boundary conditions specified on the set of possible contact include constraints on deflections in the form of inequalities that do not allow mutual penetration of bodies. In this case, the set of contact points of the bodies is not known in advance, and thus the considered contact problems belong to the class of nonlinear problems with a previously unknown boundary.
A. M. Khludnev and his students I. V. Fankin and A. I. Furtsev are participants in the research project "Differential Equations and Dynamical Systems" of the Mathematical Center in Akademgorodok.