1972

Was born in Moscow.

1989-1995

Student of the Department of Differential Equations and Mathematical Physics (DDEMP), Faculty of Applied Mathematics and Physics, Moscow State Aviation Institute (Technical University) (MAI).

1998

Defended his Postgraduate diploma. PhD thesis : "Some classes of non-local elliptic problems and Feller semigroups", Faculty of Computational Mathematics of M.V. Lomonosov Moscow State University.

1998-2000

Assistant at DDEMP, MAI.

1999

Intern at the Department of Mathematics, University of Trieste (Italy).

2000-2006

Assistant at the Department of Functional Analysis, University of Rostock, Germany.

2006

Received Dr. rer. nat. habil. degree, thesis theme: “Positive Solutions of Some Partial Differential Inequalities and Systems” at the University of Rostock, Germany.

2006-2009

Assistant professor at DDEMP, MAI. Doctoral student of the department of theory of functions at the V.A. Steklov Mathematical Institute, Russian Academy of Sciences (RAS).

2010

Defended his Doctoral thesis. Dr.Sci. thesis : "On the blow-up of solutions of nonlinear singular partial differential equations", V.A. Steklov Mathematical Institute, Russian Academy of Sciences (RAS).

2009-2018

Associate Professor of the Department of Mathematical Analysis and Theory of Functions of the RUDN University.

2017

Deputy Director of the S. Nikolsky Mathematical Institute.

Since 2018

Associate professor at  the  S. M. Nikolskii Mathematical Institute.

Teaching

  1. Developer of educational courses, the most significant are the following:
    • “Destruction of solutions of nonlinear inequalities” (Scientific and Educational Center at the V.A. Steklov Mathematical Institute, 2009)
    • "Modern problems of mathematics" (RUDN University, 2017)
    • “Destruction of solutions of nonlinear differential inequalities” (RUDN University, 2018)
  2. In 2006 conducted the “Functional Analysis” lecture course in German (“Mathematics” direction, bachelor degree) at the University of Rostock (Germany)
  3. In 2014 conducted the “Theory of Functional Spaces” course of lectures (“Mathematics” direction, magistracy) at RUDN University
  4. Teaches the following disciplines at RUDN University:
    • "Mathematical analysis" ("Fundamental informatics and information technology", "Mathematics and computer science" directions, bachelor degree, lectures),
    • "Functional analysis" ("Mathematics" direction, bachelor degree, practical classes in Russian and English),
    • "Modern problems of mathematics" (“Mathematics” direction, master's, lectures and practical classes),
    • “Destruction of solutions of nonlinear differential inequalities” (“Mathematics” direction, Master's program, lectures and practical classes)

Science

  • As a student, under the leadership of Alexander L. Skubachevsky, investigated differential operators with non-local conditions and obtained the geometric characteristics of their spectrum, which can be used to calculate distributed loads in aircraft engineering, machinery, etc.
  • Studied Feller semigroups generated by elliptic operators with nonlocal conditions, and obtained sufficient conditions for the existence of these semigroups. The theory of Feller semigroups is used in the study of multidimensional diffusion processes in biological cells.
  • Since 1999 (together with the scientific groups of Enzo Mitidieri and Stanislav I. Pokhozhaev), and since 2011 (together with Olga A. Salieva and other co-authors) has investigated the solvability of nonlinear differential and functional differential equations and inequalities. Sufficient conditions for the absence of solutions (catastrophes) for equations and inequalities containing coefficients with singularities on unbounded domains, variable nonlinearity parameters, fractional powers of the Laplace operator, etc. were obtained. For inequalities with power singularities on unbounded domains, the optimality of the conditions obtained was proved. The developed analytical and numerical methods have been used in modeling the sintering of aluminum oxide in metallurgy, the phenomena of chemotaxis and haptotaxis during the propagation of microorganisms and the growth of malignant tumors, the emergence of financial bubbles, etc.
  • Since 2009 has investigated the monotonicity of bounded positive solutions of the Dirichlet quasilinear problem in half-space. Together with Olga A. Salieva he obtained sufficient conditions for the monotony of such solutions in terms of nonlinearity indicators. It is assumed that the obtained results are used to predict the occurrence of phase transitions in an activated plasma.

Scientific interests

  • Lack of solutions of nonlinear differential and functional differential equations and inequalities.
  • Monotonicity of solutions of nonlinear boundary value problems.
  • Spectral theory of differential operators with non-local conditions.
  • Operator Feller semigroups.
We obtain sufficient conditions for the existence of a Feller semigroup generated by an elliptic operator with integro-differential boundary conditions. In this paper we study both transversal and non-transversal cases under very general assumptions on nonlocal terms.
It is shown that various quasilinear elliptic and parabolic differential inequalities and systems of such inequalities defined on bounded domains, and which have point singularities on the boundary do not have solutions. The method of nonlinear capacity is used in the proof. Examples show that the conditions obtained by this method cannot be improved in the class of problems under consideration.
By the nonlinear capacity method, conditions of solvability are obtained for some classes of stationary and evolutional differential inequalities with coefficients that have singularities on unbounded sets.
We consider a nonlinear PDEs system of two equations of Parabolic–Elliptic type with chemotactic terms. The system models the movement of a biological population towards a higher concentration of a chemical agent in a bounded and regular domain. We study the range of parameters and constrains for which the solution exists globally in time.