The first research school of RUDN officially formed

The head of the school is Alexander Leonidovich Skubachevsky, PhD in Physics and Mathematics, Professor, Honored Scientist of Russia. The scientific school includes 6 doctors and 16 Ph. D. and Mathematical Sciences, as well as 6 young scientists.

“In the modern world, it is incredibly difficult to achieve significant success through the efforts of one scientist, at the same time, a research school can unite talented researchers, allowing them to make breakthrough discoveries. The staff of the research school ‘Differential and Functional Differential Equations’ appreciate the Academic Council for the official consolidation of the status of the school,” said Alexander Skubachevsky.

What was done by the scientists:

• more than 700 works have been published, 80 of them in the last 3 years in the best Russian and international journals;
• 5 grants were received for research in the last 3 years;
• 7 monographs and 16 textbooks were written;
• more than 15 international conferences were organized, as a result of which collections of scientific publications have been published;
• 6 PhD theses have been defended in the last 5 years;
• The doctoral dissertation of P.L. Gurevich and the PhD dissertation of Yu.O. Belyaeva were recognized by the Higher Attestation Commission as the best in Russia in the field of mathematics in 2008 and 2019, respectively.

The main scientific directions:

• Boundary-value and mixed problems for elliptic and parabolic differential and functional-differential equations;
• Nonlocal boundary value problems;
• Kinematics Equations;
• Cauchy problem for parabolic type equations with differential operators and shift operators;
• “Destruction” theory of the solution of a strongly nonlinear equation;
• Machine learning, artificial neural networks.

The research school’s history

The research school of Professor Lev Ernestovich Elsgolts was the first research school in the world in the field of functional-differential equations and the first seminar in this field in the world. The seminar was organized in 1950 at the Faculty of Physics of the Moscow State University. After, in 1960 Professor Lev Elsgolts and his students moved to the Patrice Lumumba Peoples’ Friendship University, his research seminar was moved there as well. One of L. Elsgoltz’s most famous students was Professor Georgii Alexandrovich Kamenskii, who continued to lead the scientific seminar. The current head of the research school is Alexander Leonidovich Skubachevsky, he is one of Professor G.A. Kamensky’s students.

The moment of creation of the school can be considered the beginning of the scientific seminar “Differential and functional differential equations” under the leadership of Alexander Skubachevsky in September 1988.

Since 1994, international conferences on differential and functional differential equations have been held under the leadership of A.L. Skubachevsky. The conferences of 2002 and 2014 are recognized as satellites of the International Congress of Mathematicians.

In 2005, the Department of Differential Equations and Mathematical Physics was established at RUDN. School continues to work in the areas of the scientific school, such as: studies of kinetic equations, nonlocal boundary value problems, Cauchy problems, nonlinear inequalities, and others.

The school’ s scientific achievements:

• For the first time the necessary and sufficient conditions for hyperbolicity of periodic solutions for nonlinear functional-differential equations were obtained (together with the famous German mathematician H.-O. Walter).
• The theory of linear boundary value problems for elliptic and parabolic functional differential equations is constructed, which has found application in the study of elastic deformations of multilayer plates and shells, as well as in the theory of elliptic problems with non-local conditions.
• New conditions for the occurrence of self-oscillations in nonlinear optical systems with two-dimensional feedback are obtained, which are described by quasi-linear parabolic functional differential equations.
• The Cauchy problem for differential-differential parabolic equations as well as for singular functional-differential parabolic equations containing Bessel operators, shift operators and (integral) generalized shift operators is investigated.
• Mixed and non-local problems for the system of Vlasov-Poisson equations in a half-space and an infinite cylinder with an external magnetic field are considered. This problem describes the kinetics of charged particles in high-temperature plasma in installations performing controlled thermonuclear fusion. It is shown that under the action of a sufficiently large external magnetic field, the characteristics of the Vlasov equations do not cross the boundary of the regions under consideration.

What criteria should the RUDN research school meet?

• Several generations of scientists led by one (or several) scientific leader(s);

• Postgraduate studies, doctoral studies in the profile of the school, preparation of Doctor of Sciences in the scientific profile of the school, including its head;

• Dissertation Council on the scientific specialty of the school;

• The presence of doctors working at the university on a permanent basis on a general topic together with the head;

• Preparation of candidates of sciences from among the full-time staff and graduate students of the RUDN in the school team;

• Availability of monographs or textbooks/teaching aids;

• Receiving international or Russian grants for scientific research;

• The volume of attracted external financing for the implementation of fundamental and applied scientific research;

• The number of prestigious international and/or All-Russian scientific and practical conferences of the RUDN with the publication of a collection of works;

•  Availability of publications in scientific publications indexed in Web of Science / Scopus, including in highly rated journals of the first and second quartiles;

• Conducting public master classes, scientific seminars, including permanent international seminars.