1981

Graduated with honors from the Peoples’ Friendship University named after Patrice Lumumba  in the specialty  of  «Mathematics».  He was awarded  the qualification of «Mathematician. Lecturer of mathematics  in higher and secondary learning establishments». He was also awarded  the qualification  of «Translator from French into Russian».

1981-1984

Post-graduate student at the P. Lumumba Peoples’ Friendship University.

1984

Candidate thesis “Method of Ostrogradskii and inverse problems of mechanics” was defended.

1984-1987

Staff member of the computing center of the Peoples’ Friendship University, senior lecturer.

1987-1988

Scientific trip to the University of California, Santa Barbara (USA).

1988-1993

Senior lecturer, associate professor in the Department of Mathematics and Informatics at the P. Lumumba Peoples’ Friendship University.

1992

Doctoral thesis “Mathematical methods of mechanics of infinite-dimensional non-potential systems” for the degree of Doctor of Physics and Mathematics was defended at the M.V. Lomonosov Moscow State University.

1993-2005

Professor in the Department of Mathematical Analysis.

1995

Academic title Professor was awarded.

2005-2018

Professor in the Department of Mathematical Analysis and Theory of Functions.

2018 - present time

Professor of the S.M. Nikol’skii Mathematical Institute.

2010

Gratitude of the Federal Agency for Education.

2013

The breastplate and honorary title “Honorary worker of higher professional education of the Russian Federation”.

2017

Honorary badge “Veteran of the RUDN”.

Teaching

  1. V.M. Savchin worked out a number of new special courses for master's students, in particular:
    • “Variational methods for the study of operators” (direction “Functional Methods in Differential Equations and Interdisciplinary Research”),
    • “Inverse problems of the calculus of variations” (direction “Functional Methods in Differential Equations and Interdisciplinary Studies").
  2.  Courses at the RUDN University:
    • “Mathematical analysis” (direction “Applied Mathematics and Informatics”) for bachelor’s students,
    • “Inverse problems of the calculus of variations” (direction “Functional Methods in Differential Equations and Interdisciplinary Research”) for bachelor’s students.

Science

Author of monographs:

  • Mathematical methods of mechanics of infinite-dimensional systems. M.: UDN, 1991, 237 p.,
  • Variational principles for nonpotential operators //Results of science and technology. Contemporary Problems of Mathematics. Latest Achievement. M.: VINITI, 1992.Vol. 40. p. 3-178 (co-authors: Filippov V. M., Shorokhov S. G.) (translated and published in the USA).
  • Research is closely linked with the works by G. Helmholtz, G. Birkhoff et al. on variational principles for finite-dimensional systems. The problem of the extension and development of their results to the case of infinite-dimensional systems was of theoretical and practical interest. It is interrelated with the problems of modern Hamiltonian mechanics, the existence of solutions to inverse problems of the calculus of variations for given equations and such algebraic structures as Lie algebras and Lie-admissible algebras. Major works are devoted to development of mathematical methods  of  mechanics of infinite-dimensional systems, development of methods for constructing variational formulations of the equations of motion of infinite-dimensional nonpotential systems and their application to such specific problems as the representation of evolution equations in the form of Hamilton's equations, the introduction of Poisson brackets and symmetric brackets in Eulerian and  non-Eulerian classes of functionals, the search of  algebraic structures associated with the equations of motion, finding symmetries and first integrals of evolution equations.

V.M.Savchin:

  • Obtained a general criterion for the B-potentiality of operators with respect to local bilinear forms.
  • Developed constructive methods of determination of integral variational principles for wide classes of equations of motion of infinite-dimensional nonpotential systems using Eulerian and non-Eulerian classes of functionals.
  • Established the connection of equations of motion of nonpotential systems with different Poisson brackets and Lie-admissible algebras and on this basis extended the scope of application of classical Hamilton's mechanics.
  • Obtained the operator equation - an analogue of ordinary Birkhoff’s differential equations - and established its significance  in the mechanics of infinite-dimensional systems. Found  the necessary and sufficient conditions for the representation of the given evolutionary equations in the form of  Birkhhoff’s operator equation and obtained the formulas for the construction of the corresponding operators.
  • Extended the methods of investigation of canonical equations of the rank greater than zero to infinite-dimensional nonpotential systems.
  • For the first time ever formulated the inverse problem of the calculus of variations for a very general system of partial differential difference equations and obtained the conditions of its potentiality.
  • Worked out an operator approach providing a unique methodology for the investigation of a number of properties of the equations of motion of both finite dimensional and infinite-dimensional systems.     
  • Theoretical results are applied, in particular, to the system of Navier-Stokes equations describing the flow of liquids, to the Korteweg-de-Vries equation describing nonlinear waves, in studies of a number of dissipative systems.

Scientific interests

  • variational principles for nonpotential operators,
  • inverse problems of variational calculus,
  • symmetries,
  • the relationship of dynamical systems with algebraic structures.
One presents numerous approaches for the construction of variational principles for equations with operators which, in general, are nonpotential. One considers separately linear and nonlinear ordinary differential equations, partial and integropartial differential equations. One constructs and investigates both extremal and stationary variational principles and one gives applications of these principles in theoretical physics and in analytic mechanics. A series of unsolved problems are indicated. The survey is intended for mathematicians, physicists, working in both theoretical and applied areas, as well as for graduate students of physics and mathematics.
There is suggested the notion of Вu-potentiality of operator N with respect to local bilinear form, and necessary and sufficient conditions of such generalized potentiality are obtained. Formulas for the construction of the corresponding integral variational action are given. Theoretical results are illustrated by two examples.
In the terms of neсessary and sufficient condition there is established the structure of operators of the given evolution equation admitting the direct variational formulation with respect to the fixed bilinear form and the symmetric operator d/dt.
There is described a quite general structure of Lie-admissible algebra in a space of Gâteaux differentiable operators. It is a natural generalization of Lie-bracкets.
There is constructed a semibounded functional whose minimum is attained on the solutions of the boundary value problem for the nonlinear unsteady Navier - Stokes equations.
Using methods of nonlinear functional analysis there is established the structure of the given type of evolution operator equation admitting the direct variational formulation.
Using methods of nonlinear functional analysis, we define the structure of an evolution operator equation of second order that can be formulated in direct variational terms.
The existence of direct variational formulations for a wide class of second order evolutionary equations is investigated.
The problem of existence of variational principles for wide classes of generally nonlinear differential-difference equations with nonpotential operators is investigated.
We establish a connection between symmetries of functionals and symmetries of the corresponding Euler–Lagrange equations. A similar problem is investigated for equations with quasi-B u-potential operators.