Mathematical problems in the dynamics of nuclear reactors. (Q2785525)

The monograph consists of three parts: I. Fundamental mathematical tools. II. Physical processes in the active zone of a nuclear reactor and their mathematical modeling. III. Investigation of nonlinear mathematical models of dynamics of nuclear reactors. NEWLINENEWLINENEWLINEPart I consists of two chapters: Chapter 1 contains an exposition of some topics of functional analysis. Chapter 2 is devoted to the explanation of problems of the qualitative theory of nonlinear equations in Banach space.NEWLINENEWLINENEWLINEPart II gives a short explanation of basic physical ideas concerning the processes under investigation and principles of their mathematical modeling. Chpater 3 presents a general description of physical processes in the active zone of a nuclear reactor, introducing the concept of a dynamical system, and considering the principle of backward coupling and modeling of systems possessing backward couplings. Chapters 4 and 5 contain linear mathematical models of basic processes without a backward coupling in the active zone of a reactor. Chapter 4 considers neutron transport and Chapter 5 processes of changes of configuration of nuclei and thermal exchange.NEWLINENEWLINENEWLINEPart III contains two chapters. In Chapter 6 a general model of dynamics is presented. In Chapter 7 concrete nonlinear models of dynamics and kinetics of a nuclear reactor on thermal neutrons are presented.