The theory of the strong interaction of thin-walled structures with liquid and gas, taking into account large displacements of the contact surface, was developed. The models of engines, pipelines, parachutes, superconducting cable, biological envelopes are investigated. Algorithms for calculating the strength of shells of complex geometry under the action of intense thermal-force loads, a method for determining the mechanical properties of films and membranes of heterogeneous structure have been developed.

Intensive nonlinear gas oscillations and aerosol deposition in pipes, particles motion in a wave field are theoretically and experimentally investigated. Nonstationary outflow of boiling fluids from pipelines, wave propagation in bubbly liquids and gas mixtures were studied. The stability of strong compression of a gas cavity in a liquid is investigated.

Methods for identifying the filtration parameters of oil, gas and water reservoirs have been developed, models of reservoir flooding using polymer-dispersed systems, gas hydrate dissociation have been constructed. Mathematical models of heat and mass transfer in heat exchangers and filters of technological installations are created.

Relativistic dynamics of the variable mass of rest is developed. The Lyapunov vector function method is developed to study of the stability of nonlinear control systems and systems with random structural changes.

The Institute take part in the work on grants from the Russian Science Foundation, the Russian Foundation for Basic Research. The works of young scientists are supported by grants of the President of the Russian Federation, prizes of the Tatarstan Republic.

The research results of the Institute are used in practice. For Gazprom Transgaz Kazan, a mathematical model has been created for estimating of the stresses concentration on sections of pipelines, and active linings have been developed for the “treatment” of pipeline defects. By agreement with the company TATNEFT, a method for determining the filtration parameters of gas and oil reservoirs was developed and introduced; thermo-hydrodynamic studies of vertical wells exploiting multilayer objects were performed. By agreement with the company Nizhnekamskneftekhim, new sprinklers and drift catchers were developed and installed on cooling towers, increasing the degree of water cooling; filters for purification of recycled water from mechanical impurities are introduced; the state of the buildings of the cooling towers surveyed with the installation of the support system. Developed filters for the purification of recycled water are installed at the Kazanorgsintez company.