Search academic texts

Information × Registration Number 0220U101342, 0119U102376 , R & D reports Title Qualitative, asymptotic and numerical analysis of various classes of differential equations and dynamical systems, their classification, and practical application popup.stage_title Head Filipkovskaya Mariya S., Кандидат фізико-математичних наук Registration Date 10-02-2020 Organization B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine popup.description2 The theorems on the existence and uniqueness of global solutions of non-stationary degenerate differential equations (non-stationary differential-algebraic equations) were obtained. The theorems on the Lagrange stability, the Lagrange instability, and the asymptotic stability of non-stationary degenerate differential equations were also obtained. Two combined numerical methods for solving degenerate differential equations were developed, and their convergence was proved. The comparative analysis of these methods was carried out and conclusions about the effectiveness of their application in various situations were made. The sufficient conditions under which Cantor dynamical systems of infinite rank have a prescribed number of probability ergodic invariant measures were found. The wide class of Bratteli-Vershik systems modeling aperiodic homeomorphisms of Cantor sets was introduced, and the supports of their ergodic invariant measures were described in terms of the corresponding subdiagrams of Bratteli diagrams. An effective boundary value problem for the system of Maxwell equations on a virtual tape surface was obtained, and the system of boundary integral equations of the obtained averaged problem was constructed.  Product Description popup.authors popup.nrat_date 2020-04-02 Close