Division of Mathematical Modeling

The Department of Mathematical Modeling conducts scientific research in the broadly understood theory of modeling of evolutionary processes occurring in the exact and natural sciences.  This includes an analysis of their stationary states and topics of process control and their optimization from the point of view of various quality criteria. Such problems are generally described by ordinary or partial differential equations, functional differential equations, integral equations, and difference equations (for discrete processes) under the presence of local or nonlocal boundary conditions. Research concerns fundamental problems in the field of functional analysis, operator theory, operator semigroup theory, calculus of variations and variational methods, theory of dynamical systems, fixed point theory and topology. In particular, the research covers questions about the existence, multiplicity, structure, asymptotic behaviour and stability of solutions, and other quality problems. The research also covers applications and quantitative issues. In particular, studies of modeling dynamic processes and systems in medicine (e.g., epidemiological and transmission models, drug therapy models) and in biology (e.g., the description of fragmentation, coagulation, population and ecological processes) are pursued in this department.