During my stay at the Institute of Analysis and Scientific Computing, I studied the qualitative behavior of solutions of abstract differential-algebraic equations (ADAEs) as well as mathematical models in the form of ADAEs which arise in electronics and gas industry. I mainly focused on the mathematical model of an electrical network coupled to a meristor. It is described by a system of partial differential equations (PDEs) and differential-algebraic equations (DAEs) and can be represented as an ADAE (such an ADAE is often called a PDAE). For ADAEs of a semilinear type, I obtained theorems on the existence and uniqueness of solutions, the maximal interval of existence of a solution, the global solvability, the boundedness of solutions and the blow-up of solutions.

I currently work at B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine (B. Verkin ILTPE of NAS of Ukraine) as a Senior Research Fellow. I continue the research that I conducted at TU Wien, namely, I study ADAEs and their applications and develop numerical methods for ADAEs. Among the applications that I am currently considering, the main ones are still models of memristor devices coupled to electrical networks. Also, I plan to continue my research related to the analysis of asymptotic behaviour of solutions of nonlinear integrable PDEs arising, for example, in nonlinear optics. In addition, I plan to study various types of stability of control systems modeled by DAEs and ADAEs (or PDAEs).