Mathematical modeling, nonlinear equations of evolution, and the dynamics of nuclear reactors

The article presents some results on solvability and qualitative properties of solutions of the abstract Cauchy problem for a new class of nonlinear equations of evolution in Banach spaces. These results provide a unified framework for the analysis of a wide range of applied problems. Some applications to nonlinear mathematical problems of nuclear reactor dynamics are suggested. Supported by a grant from the Ministry of Science, Higher Education, and Technical Policy of the Russian Federation as part of the program, “Nonlinear Dynamic Systems: Qualitative Analysis and Control.” Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 76–90, 1994.