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Information × Registration Number 0308U003083, 0106U001535 , R & D reports Title Asymptotic and qualitative behaviour of solutions to dissipative evolution equations with partial derivatives popup.stage_title Граничні рівняння у задачах коливання шматково-однорідних пластин Head Chueshov I., Registration Date 29-02-2008 Organization Kharkov national university named after V.N. Karazin popup.description2 Research report: p. 23, references 22. Objects of the research are qualitative methods of studying of initial-boundary value problems of mathematical physics. Pseudodifferential boundary equations arising in theory of bending of piecewise homogeneous thermoelastic plates are studied. The goal of the work is reduction of original initial-boundary value problems of Nuemann or Dirichlet type (both internal and external) which arise in theory of bending of piecewise homogeneous thermoelastic plates with transverse shear effect to a system of dynamic pseudodifferential boundary equations and proof of unique solvability of the abovementioned equations in a scale of Sobolev type spaces. Representation of solutions of the original thermoelastic problems as a sum of single and double layer potentials is found, that leads to the boundary pseudodifferential equations system with respect to unknown densities of potentials; thus, the problem dimension is reduced by one. Existence, uniqueness and stability of solutions to the boundary equations system in a scale of Sobolev spaces are proved. Reseach method is theoretical constructions. The work is of theoretical nature. The results may be used for construction of algorithms of approximate description of thermoelastic plates oscillations. THERMOELASTISITY, BOUNDARY DIFFERENTIAL EQUATIONS, DYNAMICAL POTENTIALS, TRANSVERCE SHEAR EFFECT Product Description popup.authors popup.nrat_date 2020-04-02 Close