Mathematics and modeling for the study of natural phenomena.
Graduated with honors from the Faculty of Mechanics and Mathematics of the Southern Federal University (SFU, Rostov–on-Don).
PhD. thesis “Autowave processes in chemically active media”.
Worked at the Institute of Chemical Physics of the USSR Academy of Sciences (Chernogolovka), worked his way up from engineer to head of the laboratory of Macrokinetics of polymerization processes.
Schelkin prize of the Soviet Academy of Sciences.
Visiting researcher at the Courant Institute Mathematical Sciences, New York University, USA.
Research Fellow, Department of Materials Science, Northwestern University, USA.
Works at the French National Center for Scientific Research (Directeur de recherche, Centre National de la Recherche Scientifique) and at University Lyon 1, France.
Habilitation, “Mathematical theory of reaction-diffusion equations and their application in chemical physics”, University Lyon 1.
Deputy Director of Camille Jordan Institute, Lyon, France.
Member of the board of Directors of the Institute for Systems Biology and Medicine, Lyon, France.
Member of the Council of the European Society for Theoretical and Mathematical Biology.
Director of the interdisciplinary research center “Mathematical modeling in Biomedicine” of S.M. Nikol’skii Mathematical Institute of RUDN.
Member of editorial boards of the following journals:
- Mathematical modelling of natural phenomena (founder and editor-in-chief, 2006),
- Complex variables and elliptic equations (2017),
- Computation (2018),
- Computer research and modelling (2018),
- Pure and Applied Functional Analysis (2016),
- Mathematics (2019).
- Gives the course of lectures “Reaction-diffusion equations and applications” for postgraduate students of the direction “Differential equations, dynamical systems and optimal control”.
- 2014 - 2018 gave courses on partial differential equations and mathematical modeling to students, postgraduate students at the Faculty of Mathematics at the Higher school of Kouba. (Ecole Normale de Kouba, Algeria) and other educational institutions in Algeria.
- 2017 gave courses on partial differential equations and mathematical modeling to students, postgraduate students at the Faculty of Mathematics of the National Institute of Technology Patna, India.
- 2012 - 2013 gave courses on partial differential equations and mathematical modeling to students at the Engineering Faculty of Ecole Centrale de Lyon France.
- Repeatedly was invited for scientific visits and lectures to England, Israel, India, Poland, USA, Chile and other countries. Last three years:
- 2018 - University of Talca (Chili), University of Warsaw (Poland), University of Tlemcen (Algeria)
- 2017 - King’s college London (UK), University of Tlemcen (Algeria), University of Talca (Chili), Baumann University Moscow (Russia), Indian Institute of Technology Patna (India)
- 2016 - University of Leiden (Netherlands), University of Talca (Chili), Institute of numerical mathematics, Moscow (Russia)
- Elliptic problems in unbounded domains were studied. Fredholm conditions for general elliptic operators in unbounded domains were obtained. Solvability conditions of linear problems, index, solvability conditions for non-Fredholm operators were studied. Property conditions of general nonlinear elliptic operators in unbounded domains were obtained and a topological degree was constructed.
- Reaction-diffusion waves, in particular, existence and stability of waves for monotonic and locally monotonic systems, minimax representation of wave velocity were studied. Application to various problems of chemical kinetics, population dynamics, biomedicine. Generalized travelling waves.
- Nonlocal reaction-diffusion equations and equations with delay were studied. Local and global stability of equilibrium states, existence of travelling waves and generalized travelling waves, bifurcations and nonlinear dynamics were studied. Applications to various problems of population dynamics and biomedicine.
- Waves in combustion and chemical kinetics, the existence, stability, bifurcations, nonlinear dynamics were studied. Thermal explosion with convection, thermal explosion conditions, convection influence, space-time structures, vibrational thermal explosion, thermal explosion in porous medium were studied.
- Existence, stability, propagation velocity, nonlinear dynamics of front polymerization waves were studied. Production technology of poly-epsilon-caprolactam based on frontal polymerization. Influence of convection on the propagation of frontal polymerization waves was studied. Low-temperature waves accompanied by the destruction of a solid.
- Interphase and capillary phenomena in miscible liquids were studied, and experiments on the international space station were prepared.
- Mathematical modeling of atherosclerosis. Models of atherosclerosis as a chronic inflammation of the artery walls were developed. Development of atherosclerosis depending on the cholesterol content was studied. Development of atherosclerosis as a reaction-diffusion wave. Existence and stability of waves in one-dimensional formulation and in two-dimensional formulation with nonlinear boundary conditions were investigated. Interaction of an atherosclerotic plaque with the flow.
- Blood clotting and comorbidities. Different modes of blood clotting and conditions of their implementation. Blood clotting as a reaction-diffusion wave. Existence, stability and speed of propagation. Initial conditions for initiation of coagulation and existence of a solution in the form of a stationary pulse. Influence of various factors on clotting: blood flow, platelets, inflammation. Thrombosis and bleeding. Identification of patients with hemophilia.
- Modeling of cancer: leukemia and multiple myeloma. Development of mathematical models, analysis and numerical modeling, characterization of myeloblastic leukemia by flow cytometry. Modeling of the development of multiple myeloma. Selection of optimal treatment protocols.
- Mathematical modeling of erythropoiesis. Development of hybrid models of erythropoiesis taking into account the presence of cells of different types, intracellular and intercellular regulation. Functioning of erythroblastic islets and production of erythrocytes, reaction to hypoxia, regulation by erythropoietin.
- Mathematical immunology. Development of viral infection as a reaction-diffusion phenomenon. Existence, resistance and modes of spread; influence of delayed immune response; virus mutations; antiviral therapy and emergence of resistant strains.
- Electrical stimulation of the cerebral cortex for rehabilitation of patients after stroke. Modeling of electric potential waves in the cerebral cortex on the basis of integro-differential equations of the mean field theory. Different wave propagation modes, stability, bifurcations, nonlinear dynamics. Selection of stimulation modes to restore waves characteristics in damaged areas of the brain.
- Development of hybrid models in biomedicine based on the combination of discrete cell models and continuous models for intracellular regulation (ODE) and intercellular regulation (PDE). Application to various problems of biomedicine (leukemia, lymphoma, myeloma, erythropoiesis). Hybrid models with dissipative particle dynamics to study blood flow clotting.
- Evolution of biological species. Development of models of evolution based on nonlocal reaction-diffusion equations, taking into account competition for resources. Conditions of emergence of new species, description of different modes of evolution of species. Interrelation of different definitions of species (by Darwin and Mair). Nonlocal predator-prey models.
- Morphogenesis and modeling of plant growth. Development of plant growth models, how to explain plant diversity, branching; vegetative hormones and nutrients. Two-dimensional models based on cell division, plant growth as self-similar structures. Different models of morphogenesis and wound healing.
- Other issues: economic and demographic models, phase transitions in metal oxides, propagation of calcium waves, etc.
- General theory of elliptic equations in unbounded domains;
- Mathematical theory of reaction-diffusion waves with applications in chemical kinetics and combustion;
- Nonlocal reaction-diffusion equations and equations with delay;
- Vibrational thermal explosion;
- Capillary phenomena in miscible fluids;
- Mathematical theory of the origin and evolution of species;
- Mathematical theory and modeling of biomedical processes: atherosclerosis and other chronic inflammations, blood clotting and thrombosis, cancer;
- New methods of mathematical modeling in Biomedicine;
- The study of mathematical models of various biological and ecological issues: plant growth, morphogenesis, etc.