The main idea of the project: research of new classes of differential and functional-differential equations, inequalities and systems and the application of the obtained results to interdisciplinary research in mathematical models of physical and biological processes.
- A.L. Skubachevskii, A.Sh. Adkhamova. Damping Problem for a Neutral Control System with Delay. Doklady Mathematics (Q2) DOI: 10.31857/S2686954320010038
- A. Savin, E. Schrohe. Analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations. J. . Funct. Anal. 278 (2020), no. 5, 108400, 45 pp. (Q1) https://doi.org/10.1016/j.jfa.2019.108400
- N. Bessonov, G. Bocharov, A. Meyerhans, V. Popov, V. Volpert. Nonlocal reaction-diffusion model of viral evolution: emergence of virus strains. Mathematics (Q1) doi:10.3390/math8010117
- V. A. Derkach, S. Hassi, M.M. Malamud. Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions. Math. Nachr. (Q1) DOI: 10.1002/mana.201800300
- The aim of this project relate to the study of nonlocal equations and reaction equations with delay arising in biomedicine, including immunology and neurology.
- It is supposed to obtain new solutions by energy substitution under conditions of quasineutrality for the Vlasov-Poisson and Vlasov-Maxwell equations.
- One of the goals of the project is to construct a theory of boundary value problems for elliptic functional differential equations with affine transformations of independent variables.
- It is planned to study the analytical and topological aspects of the theory of nonlocal elliptic operators.
- To investigate the relationship between the scattering matrix of a pair of self-adjoint operators, whose resolvent difference is of finite order but is not nuclear. Obtain an analogue of the invariance principle of M. S. Birman and T. Kato in the considered situation. To explore the connection of this formula with trace formulas.
- It is proposed to study initial-boundary value problems for various classes of semilinear and quasilinear parabolic equations of the structure of linear and nonlinear diffusion - nonlinear absorption degenerating on various manifolds with singular boundary or initial data.