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Information × Registration Number 0216U002962, 0115U003845 , R & D reports Title Linear evolution equations in a Hilbert space and the Boltzmann equation. popup.stage_title Head Khalina Katerina Sergiivna, Registration Date 03-01-2017 Organization B.Verkin Institute for Low Temperature Physics and Engineering NAS of Ukraine popup.description2 The explicit form of the resolvent of the generator of С_0- group with complete non-basis family of eigenvectors was obtained, the growth rate of the resolvent in the neighbourhoods of spectrum was studied. Simple criteria of stability for linear evolution equations in Hilbert spaces were obtained in the case when the operator of the left-hand side of equation is closed, has a Riesz basis of eigenvectors and has no root vectors. The results were applied to the study of stability of equations with operators which have certain form of triangular infinite matrix. The results on the stability of Riesz bases, that were obtained previously by V.A. Marchenko in 2014, were improved. Bimodal distribution with Maxwell modes of the most general form for the Bryan-Pidduck equation was obtained. Infinitely-modal distributions with some Maxwell modes for the Boltzmann equation in the case of hard-spheres model were obtained. Product Description popup.authors Гукалов Олексій Олександрович Марченко Віталій Анатолійович Халіна Катерина Сергіївна popup.nrat_date 2020-04-02 Close