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Information × Registration Number 0219U001926, 0118U001778 , R & D reports Title Operator-differential equations and their applications in problems of physics popup.stage_title Head Marchenko Vitalii Anatoliyovych, Registration Date 27-03-2019 Organization B.Verkin Institute for Low Temperature Physics and Engineering NAS of Ukraine popup.description2 Simple criterions of stability, exponential and asymptotic stability of linear abstract differential equations in a Hilbert space depending on spectral properties of the corresponding unbounded nonselfadjoint operator with multiple spectrum were found. Conditins for existence and non-existence of the maximal asymptotics for equations of this type were established. Results were applied to the study of stability and question of maximal asymptotics for infinite-dimensional systems of some triangular form. The explicit form of the resolvent of the generator of strongly continuous group with non-basis family of eigenvectors was found and its spectral properties were characterized. Theorems concerning Lagrange stability and instability for semilinear differential-algebraic equations with regular and singular operator bundles, and for the class of nonstationary differential-algebraic equations were obtained. The study of mathematical problems of diffraction and scattering were performed: boundary-value problems for Helmholtz equation with additional conditions. Problems are reduced to the corresponding limit integral equations. Numerical methods of solving complete hyper singular integral equation of the second kind and systems of such equations were developed. Obtained results were applied to the solution of problems of diffrraction and scattering for electromagnetic waves in a space, divided by a periodic stripe-type lattice. Product Description popup.authors Андреєв Кирило Миколайович Костенко Олексій Володимирович Марченко Віталій Анатолійович Філіпковська Марія Сергіївна popup.nrat_date 2020-04-02 Close