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Information × Registration Number 0307U001660, 0106U001535 , R & D reports Title Asymptotic and qualitative behaviour of solutions to dissipative evolution equations with partial derivatives popup.stage_title Асимптотична поведінка розв'язків задач термопружності в постановці Міндліна -Тимошенко та термопружної пластини в дозвуковому потоці газу Head Chueshov I., Registration Date 18-04-2007 Organization Kharkov National University named after V.N.Karazin popup.description2 Object of the research are qualitative methods of study of asymptotic behaviour of solutions to initial-boundary value problems of mathematical physics. Global attractors of Mindlin-Timoshenko thermoelastic system (including the system with memory) and asymptotic behaviour of solutions to the problem of oscillations of a thermoelastic plate in a subsonic gas flow are investigated. The goal of the research are the proof of existence of a compact global attractor for Mindlin-Timoshenko themoelasticity, the proof of the reduction principle for this problem, the study of the properties of the attractor family of the problem with memory when time goes to infinity, and the proof of stabilization of solutions to the problem of oscillations of a thermoelastic von Karman plate in a subsonic gas flow. The existence of attractor for Mindlin-Timoshenko problems means that the solutions to these problems uniformly tend to a bounded compact set, and reduction principle gives us a possibility to represent a temperature as a function of the plate displacement, when describing the attractor. For the Mindlin-Timoshenko problem with memory upper semicontinuity of the attractor family is proved, provided relaxation time goes to zero. It means that the corresponding system without memory describes the behaviour of the object well enough, provided the time of relaxation is small. As for the problem of oscillations of a thermoelastic von Karman plate in a gas flow, the stabilization of the entire system is proved. That is, it is shown the triple of functions "plate displacement + plate temperature + perturbed gas flow velocity" which is the solution to the system tends to the set of stationary points of the system when the time tends to infinity. The methods of the research are theoretic constructions. The work is of theoretical nature. Its results can be used for the construction of algorithms of the approximate study of the asymptotic behaviour of nonlinear thermoelastic and aerothermoelastic systems DINAMICAL SYSTEMS, GLOBALATTRACTORS, REGULARITY, STABILIZATION, THERMOELASTICITY, AEROELASTISITY, REDUCTION PRINCIPLE. Product Description popup.authors popup.nrat_date 2020-04-02 Close