Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
20.02.1938
Keywords: differential equations and applications,
mathematical models and partial differential equations,
asymptotical methods,
mathematical education,
lattice of connected oscillators,
invariant torus,
attractor,
bufferness.
Subject:
For singularly perturbed systems of ordinary differential equations the general asymptotic theory of periodic solutions close to discontinuous solutions (modeling relaxation oscillations) is constructed; the trajectories-duck etc. problems were studied. For singularly perturbed partial differential equations the periodic motions and bifurcation processes were investigated; the theoretical justification of a new buffer phenomenon (which could be watched in many mathematical models of natural sciences and technique, which described by the hyperbolic and parabolic type equations) is gave. The investigations were realized in cooperation with E. F. Mishchenko and A. Yu. Kolesov. The results in the general and qualitative theory of the ordinary differential equations (distribution of the Lyapuniv exponents etc.), in theory of controllable systems (stabilization of non-stable non-stationary systems etc.), in theory of optimal control and differential games (investigation of an alternating Pontriagin integral etc.) are obtained, in theory of partial differential equations (the asymptotical solution of singularly perturbed equations of mixed type etc.), in applications of the differential equations (for example, to a theory of oscillations). The series of the publications is dedicated to the content and procedure of teaching of mathematics in secondary and high schools, architecture of mathematical education, history and methodology of mathematics, propaganda of mathematical knowledge among youth.
Main publications:
Mishchenko E. F., Rozov N. Kh. Differential equations with small parameters and relaxation oscillations. New York: Plenum Press, 1980. 230 pp.
Mishchenko E. F., Kolesov Yu. S., Kolesov A. Yu., Rozov N. Kh. Asymptotic methods in singularly perturbed systems. New York: Consult. Bureau, Plenum Publ. Corp., 1994. 281 pp.
Kolesov A. Ju., Mishchenko E. F., Rozov N. Kh. Asymptotic methods of invistigation of periodic solutions of nonlinear hyperbolic equations // Proc. Steklov Inst. of Math. 1998. V. 222. P. 3–188.
Dorofeev G., Potapov M., Rozov N. Elementary mathematics. M.: Mir., 1988. 490 pp.
