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Information × Registration Number 0203U008082, 0100U003363 , R & D reports Title Qualitative methods in the research of initial boundary value problems of mathematical physics popup.stage_title Head Chyeshov I., Registration Date 22-04-2003 Organization Kharkov National University named after V.N.Karazin popup.description2 Object of research is qualitative methods of study of initial-boundary problems of mathematical physics. We study global attractors of stochastic dynamical systems generated by semilinear parabolic equations with periodic boundary conditions wich is subjected to a spatially smooth additive white noise and initial-boundary problems of dynamics of thermoelastic media with cracks. The goal of the work is poof of Gevrey regularity of global attractors of stochastic dynamical systems and unique solvability thermoelastic problems under consideration in the scale of Sobolev type functional spaces. Gevrey regularity obtained means that the elemets of the attractor are real analytic functions in spatial variables, that allow as to prove existense of two determining nodes for problems in one spatial dimention. Also solutions of problems of dynamics of thermoelastic media with cracks are found. They are represented by the sum of analogues of the single and double layer potentials, that yields the system of non-stationary boudary equations. Method of research is theoretical construction. The work is of theoretical nature. It's results may be used for a construction of algorithms of approximate study of non-linear dissipative systems and for modeling of thermoelastic media with cracks. Product Description popup.authors popup.nrat_date 2020-04-02 Close