Global and numerical analysis of descriptor systems and integrable nonlinear partial differential equations and applications
Dr. M. S. Filipkovska
2022 - 2023
The aim of research was the development analytical and numerical methods for qualitative analysis of differential-algebraic equations (DAEs) and integrable nonlinear partial differential equations (PDEs), and the application of the obtained results to study the global dynamics and optimize the control of real processes and objects described by the considered equations.
DAEs arise from the modelling of various systems and processes in control problems, gas industry, mechanics, radio engineering, chemical kinetics, economics, ecology and biology. Moreover, any type of a PDE can be represented as a DAE in appropriate infinite-dimensional spaces, possibly, with a complementary boundary condition. Such an equation is called an abstract DAE or a partial differential-algebraic equation.
https://doi.org/10.1007/s10958-024-07152-7
https://doi.org/10.3842/SIGMA.2023.096
https://doi.org/10.15407/mag19.04.719