Alexander Zlotnik
- Research Professor, Leading Research Fellow:Faculty of Economic Sciences / Department of Mathematics
- Alexander Zlotnik has been at HSE University since 2010.
Education, Degrees and Academic Titles
- 1997Professor
- 1993
Doctor of Sciences* in Computational Mathematics
Computation Centre of the Siberian Branch of the Russian Academy of Sciences - 1992Associate Professor
- 1980
Candidate of Sciences* (PhD)
- 1979
Doctoral programme
Lomonosov Moscow State University - 1976
Degree in Applied Mathematics
Lomonosov Moscow State University
According to the International Standard Classification of Education (ISCED) 2011, Candidate of Sciences belongs to ISCED level 8 - "doctoral or equivalent", together with PhD, DPhil, D.Lit, D.Sc, LL.D, Doctorate or similar. Candidate of Sciences allows its holders to reach the level of the Associate Professor.
A post-doctoral degree called Doctor of Sciences is given to reflect second advanced research qualifications or higher doctorates in ISCED 2011.
Research interests
Numerical methods for solving parabolic, hyperbolic, elliptic differential equations, the Schrödinger equation, gas and hydrodynamics systems of equations: sharp and optimal error estimates, stability, the case of unbounded domains, effective implementation methods, optimal control, computer simulation.
Systems of quasilinear equations for viscous compressible gases and liquids flow: existence, uniqueness, regularity, stabilization of solutions, continuous dependence of solutions on data, homogenization, regularized systems and their properties.
Courses (2022/2023)
- Calculus (Bachelor’s programme; Graduate School of Business; 1 year, 1-4 module)Rus
- Past Courses
20234
- Article Zlotnik A. Conditions for L² -dissipativity of an explicit symmetric finite-difference scheme for linearized 2D and 3D gas dynamics equations with a regularization // Discrete and Continuous Dynamical Systems - Series B. 2023. Vol. 28. No. 3. P. 1571-1589. doi
- Article Zlotnik A., Čiegis R. On Construction and Properties of Compact 4th Order Finite-Difference Schemes for the Variable Coefficient Wave Equation // Journal of Scientific Computing. 2023. Vol. 95. No. 1. Article 3. doi
- Article Zlotnik A., Lomonosov T. On Regularized Systems of Equations for Gas Mixture Dynamics with New Regularizing Velocities and Diffusion Fluxes // Entropy. 2023. Vol. 25. No. 1. Article 158. doi
- Preprint Zlotnik A., Lomonosov T. On a Doubly Reduced Model for Dynamics of Heterogeneous Mixtures of Stiffened Gases, its Regularizations and their Implementations / Cornell University. Series arXiv "math". 2023. No. 2305.10522.
20228
- Article Zlotnik A.A. Conditions for Dissipativity of an Explicit Finite-Difference Scheme for a Linearized Multidimensional Quasi-Gasdynamic System of Equations / Пер. с рус. // Doklady Mathematics. 2022. Vol. 106. No. 1. P. 236-242. doi
- Article Zlotnik A., Fedchenko A., Lomonosov T. Entropy Correct Spatial Discretizations for 1D Regularized Systems of Equations for Gas Mixture Dynamics // Symmetry. 2022. Vol. 14. No. 10. Article 2171. doi
- Article A. A. Zlotnik, T. A. Lomonosov. On L^2-dissipativity of a linearized scheme on staggered meshes with a regularization for 1D barotropic gas dynamics equations / Пер. с рус.: A. A. Zlotnik, T. A. Lomonosov. // Computational Mathematics and Mathematical Physics. 2022. Vol. 62. No. 11. P. 1817-1837. doi
- Article A. A. Zlotnik, Chetverushkin B. N. On Second-Order Parabolic and Hyperbolic Perturbations of a First-Order Hyperbolic System / Пер. с рус. // Doklady Mathematics. 2022. Vol. 106. No. 2. P. 308-314. doi
- Article Zlotnik A., Čiegis R. On higher-order compact ADI schemes for the variable coefficient wave equation // Applied Mathematics and Computation. 2022. Vol. 412. Article 126565. doi
- Article Zlotnik A., Fedchenko A. On properties of aggregated regularized systems of equations for a homogeneous multicomponent gas mixture // Mathematical Methods in the Applied Sciences. 2022. Vol. 45. No. 15. P. 8906-8927. doi
- Article Zlotnik A.A. On the Construction of Regularized Equations of Motion for a Mixture of Viscous Incompressible Fluids / Пер. с рус. // Doklady Mathematics. 2022. Vol. 106. No. 2. P. 380-385. doi
- Article Zlotnik A.A., Fedchenko A.S. On the properties of a quasihydrodynamic system of equations for a homogeneous gas mixture with a common regularizing velocity / Пер. с рус. // Differential Equations. 2022. Vol. 58. No. 3. P. 341-356. doi
20217
- Article Zlotnik A., Čiegis R. A compact higher-order finite-difference scheme for the wave equation can be strongly non-dissipative on non-uniform meshes // Applied Mathematics Letters. 2021. Vol. 115. Article 106949. doi
- Article Zlotnik A.A., Lomonosov T.A. L^2-Dissipativity of Difference Schemes for Regularized 1D Barotropic Gas Dynamic Equations at Low Mach Numbers / Пер. с рус. // Mathematical Models and Computer Simulations. 2021. Vol. 13. No. 6. P. 1097-1108. doi
- Article Zlotnik A. On Conditions for L2-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations // Symmetry. 2021. Vol. 13. No. 11. Article 2184. doi
- Article Balashov V., Zlotnik A. On a new spatial discretization for a regularized 3D compressible isothermal Navier–Stokes–Cahn–Hilliard system of equations with boundary conditions // Journal of Scientific Computing. 2021. Vol. 86. Article 33. doi
- Article Zlotnik A., Kireeva O. On compact 4th order finite-difference schemes for the wave equation // Mathematical Modelling and Analysis. 2021. Vol. 26. No. 3. P. 479-502. doi
- Article Zlotnik A.A., Fedchenko A.S. Properties of an aggregated quasi-gasdynamic system of equations for a homogeneous gas mixture / Пер. с рус. // Doklady Mathematics . 2021. Vol. 104. No. 3. P. 340-346. doi
- Article Zlotnik A., Chetverushkin B. Spectral stability conditions for an explicit three-level finite-difference scheme for a multidimensional transport equation with perturbations / Пер. с рус. // Differential Equations. 2021. Vol. 57. No. 7. P. 891-900. doi
20209
- Article Balashov V., Zlotnik A. An energy dissipative semi-discrete finite-difference method on staggered meshes for the 3D compressible isothermal Navier–Stokes–Cahn–Hilliard equations // Journal of Computational Dynamics. 2020. Vol. 7. No. 2. P. 291-312. doi
- Article Balashov V., Zlotnik A. An energy dissipative spatial discretization for the regularized compressible Navier-Stokes-Cahn-Hilliard system of equations // Mathematical Modelling and Analysis. 2020. Vol. 25. No. 1. P. 110-129. doi
- Article Zlotnik A.A., Zlotnik I.A. Fast Fourier solvers for the tensor product high-order FEM for a Poisson type equation / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2020. Vol. 60. No. 2. P. 240-257. doi
- Article Zlotnik A., Lomonosov T. L^2-dissipativity of the linearized explicit finite-difference scheme with a kinetic regularization for 2D and 3D gas dynamics system of equations // Applied Mathematics Letters. 2020. Vol. 103. Article 106198. doi
- Article Zlotnik A.A., Lomonosov T.A. On L^2-dissipativity of a linearized explicit finite-difference scheme with quasi-gas dynamic regularization for the barotropic gas dynamics system of equations / Пер. с рус. // Doklady Mathematics. 2020. Vol. 101. No. 3. P. 198-204. doi
- Article Elizarova T., Zlotnik A. On aggregated regularized equations for homogeneous binary gas mixture flows with viscous compressible components // AIP Conference Proceedings. 2020. Vol. 2293. No. 1. P. 210016-1-210016-4. doi
- Chapter Zlotnik A. On enlarged sufficient conditions for L^2-dissipativity of linearized explicit schemes with regularization for 1D gas dynamics systems of equations, in: Differential and Difference Equations with Applications. ICDDEA 2019, Lisbon, Portugal, July 1–5 Vol. 333. Springer, 2020. doi P. 53-67. doi
- Article Zlotnik A.A., Chetverushkin B. Stability of implicit difference schemes for a linearized hyperbolic quasi-gasdynamic system of equations / Пер. с рус. // Differential Equations. 2020. Vol. 56. No. 7. P. 910-922. doi
- Article Zlotnik A. A., Chetverushkin B. N. Stability of numerical methods for solving second-order hyperbolic equations with a small parameter / Пер. с рус. // Doklady Mathematics. 2020. Vol. 101. No. 1. P. 30-35. doi
20195
- Article Zlotnik A.A., Lomonosov T.A. Conditions for L^2-Dissipativity of Linearized Explicit Difference Schemes with Regularization for 1D Barotropic Gas Dynamics Equations / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2019. Vol. 59. No. 3. P. 452-464. doi
- Article Balashov V., Savenkov E., Zlotnik A. Numerical method for 3D two-component isothermal compressible flows with application to digital rock physics // Russian Journal on Numerical Analysis and Mathematical Modelling. 2019. Vol. 34. No. 1. P. 1-13. doi
- Article Zlotnik A. On L^2-dissipativity of linearized explicit finite-difference schemes with a regularization on a non-uniform spatial mesh for the 1D gas dynamics equations // Applied Mathematics Letters. 2019. Vol. 92. P. 115-120. doi
- Article Elizarova T. G., Zlotnik A.A., Shil’nikov E. V. Regularized Equations for Numerical Simulation of Flows of Homogeneous Binary Mixtures of Viscous Compressible Gases / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2019. Vol. 59. No. 11. P. 1832-1847. doi
- Article Zlotnik A., Lomonosov T. Verification of an Entropy Dissipative QGD-Scheme for the 1D Gas Dynamics Equations // Mathematical Modelling and Analysis. 2019. Vol. 24. No. 2. P. 179-194. doi
20189
- Article Zlotnik A., Čiegis R. A "converse'' stability condition is necessary for a compact higher order scheme on non-uniform meshes for the time-dependent Schrödinger equation // Applied Mathematics Letters. 2018. Vol. 80. P. 35-40. doi
- Article Trautmann P., Vexler B., Zlotnik A. Finite element error analysis for measure-valued optimal control problems governed by a 1D wave equation with variable coefficients // Mathematical Control and Related Fields. 2018. Vol. 8. No. 2. P. 411-449. doi
- Article Elizarova T.G., Zlotnik A.A., Istomina M. Hydrodynamical aspects of the formation of spiral–vortical structures in rotating gaseous disks / Пер. с рус. // Astronomy Reports. 2018. Vol. 62. No. 1. P. 9-18. doi
- Article Vexler B., Zlotnik A., Trautmann P. On a finite element method for measure-valued optimal control problems governed by the 1D generalized wave equation // Comptes Rendus Mathematique. 2018. Vol. 356. No. 5. P. 523-531. doi
- Article Chetverushkin B. N., Zlotnik Alexander A. On a hyperbolic perturbation of a parabolic initial-boundary value problem // Applied Mathematics Letters. 2018. Vol. 83. P. 116-122. doi
- Article Zlotnik A., Lomonosov T. On conditions for L2-dissipativity of linearized explicit QGD finite-difference schemes for one-dimensional gas dynamics equations / Пер. с рус. // Doklady Mathematics. 2018. Vol. 98. No. 2. P. 458-463. doi
- Chapter Zlotnik A., Lomonosov T. On conditions for weak conservativeness of regularized explicit finite-difference schemes for 1D barotropic gas dynamics equations, in: Differential and Difference Equations with Applications Vol. 230. Springer, 2018. doi P. 635-647. doi
- Article Zlotnik A. On the energy dissipative spatial discretization of the barotropic quasi-gasdynamic and compressible Navier-Stokes systems of equations in polar coordinates // Russian Journal on Numerical Analysis and Mathematical Modelling. 2018. Vol. 33. No. 3. P. 199-210. doi
- Article Zlotnik A., Kireeva O. Practical error analysis for the bilinear FEM and finite-difference scheme for the 1D wave equation with non-smooth data // Mathematical Modelling and Analysis. 2018. Vol. 23. No. 3. P. 359-378. doi
20176
- Article Zlotnik A.A., Zlotnik I.A. A Fast Direct Algorithm for Implementing a High-Order Finite Element Method on Rectangles as Applied to Boundary Value Problems for the Poisson Equation / Пер. с рус. // Doklady Mathematics. 2017. Vol. 95. No. 2. P. 129-135. doi
- Article Balashov V., Zlotnik Alexander, Savenkov E. Analysis of a regularized model for the isothermal two-component mixture with the diffuse interface // Russian Journal on Numerical Analysis and Mathematical Modelling. 2017. Vol. 32. No. 6. P. 347-358. doi
- Article Zlotnik A. A., Chetverushkin B. N. Entropy Balance for the One-Dimensional Hyperbolic Quasi-Gasdynamic System of Equations / Пер. с рус. // Doklady Mathematics. 2017. Vol. 95. No. 3. P. 276-281. doi
- Article A.A. Zlotnik. Entropy-Conservative Spatial Discretization of the Multidimensional Quasi-Gasdynamic System of Equations / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2017. Vol. 57. No. 4. P. 706-725. doi
- Article Chetverushkin B. N., Zlotnik A.A. On some properties of multidimensional hyperbolic quasi-gasdynamic systems of equations // Russian Journal of Mathematical Physics. 2017. Vol. 24. No. 3. P. 299-309. doi
- Chapter Zlotnik Alexander. Well-posedness of the IBVPs for the 1D viscous gas equations, in: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Cham, Switzerland: Springer, 2017. doi P. 1-73. doi
20164
- Article A.A. Zlotnik. On Conservative Spatial Discretizations of the Barotropic Quasi-Gasdynamic System of Equations with a Potential Body Force / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2016. Vol. 56. No. 2. P. 303-319. doi
- Article A.A. Zlotnik. On New Spatial Discretization of the Multidimensional Quasi-Gasdynamic System of Equations with Nondecreasing Total Entropy / Пер. с рус. // Doklady Mathematics. 2016. Vol. 94. No. 1. P. 423-429. doi
- Chapter Zlotnik Alexander, Gavrilin Vladimir. On a conservative finite-difference method for 1D shallow water flows based on regularized equations, in: Mathematical Problems in Meteorological Modelling. Mathematics in Industry Vol. 24. Berlin : Springer, 2016. doi P. 3-18. doi
- Article Zlotnik Alexander, Zlotnik Ilya. Remarks on discrete and semi-discrete transparent boundary conditions for solving the time-dependent Schrödinger equation on the half-axis // Russian Journal on Numerical Analysis and Mathematical Modelling. 2016. Vol. 31. No. 1. P. 51-64. doi
20157
- Chapter Zlotnik A. Error Estimates of the Crank-Nicolson-Polylinear FEM with the Discrete TBC for the Generalized Schrödinger Equation in an Unbounded Parallelepiped, in: Finite Difference Methods, Theory and Applications 6th International Conference, FDM 2014, Lozenetz, Bulgaria, June 18-23, 2014, Revised Selected Papers Vol. 9045. Zürich : Springer, 2015. doi P. 129-141. doi
- Article Zlotnik A., Romanova A. On a Numerov-Crank-Nicolson-Strang scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip // Applied Numerical Mathematics. 2015. Vol. 93. P. 279-294. doi
- Article Ducomet Bernard, Zlotnik Alexander, Romanova Alla. On a splitting higher-order scheme with discrete transparent boundary conditions for the Schrödinger equation in a semi-infinite parallelepiped // Applied Mathematics and Computation. 2015. Vol. 255. P. 195-206. doi
- Article V.A. Gavrilin, A.A. Zlotnik. On spatial discretization of the one-dimensional quasi-gasdynamic system of equations with general equations of state and entropy balance / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2015. Vol. 55. No. 2. P. 264-281. doi
- Chapter Zlotnik Alexander, Ducomet Bernard, Zlotnik Ilya, Romanova Alla. Splitting in Potential Finite-Difference Schemes with Discrete Transparent Boundary Conditions for the Time-Dependent Schrödinger Equation, in: Numerical Mathematics and Advanced Applications - ENUMATH 2013 Vol. 103. Springer, 2015. P. 203-211. doi
- Article Zlotnik Alexander, Zlotnik Ilya. The High Order Method with Discrete TBCs for Solving the Cauchy Problem for the 1D Schrὅdinger Equation // Computational Methods in Applied Mathematics. 2015. Vol. 15. No. 2. P. 233-245. doi
- Article Zlotnik Alexander. The Numerov-Crank-Nicolson Scheme on a Non-Uniform Mesh for the Time-Dependent Schrödinger Equation on the Half-Axis // Kinetic and Related Models. 2015. Vol. 8. No. 3. P. 587-613. doi
20142
- Article Elizarova T.G., Zlotnik A.A., Chetverushkin B. N. On quasi-gasdynamic and quasi-hydrodynamic equtions for binary mixtures of gases / Пер. с рус. // Доклады Академии наук. 2014. Vol. 90. No. 3. P. 1-5. doi
- Article Ducomet Bernard, Zlotnik Alexander, Zlotnik Ilya. The splitting in potential Crank-Nicolson scheme with discrete transparent boundary conditions for the Schrödinger equation on a semi-infinite strip // ESAIM: Mathematical Modelling and Numerical Analysis. 2014. Vol. 48. No. 6. P. 1681-1699. doi
20132
- Article Zlotnik A., Koltsova N. A family of finite-difference schemes with discrete transparent boundary conditions for a parabolic equation on the half-axis // Computational Methods in Applied Mathematics. 2013. Vol. 13. No. 2. P. 119-138. doi
- Article Zlotnik Alexander, Ducomet B. On a regularization of the magnetic gas dynamics system of equations // Kinetic and Related Models. 2013. Vol. 6. No. 3. P. 533-543. doi
20124
- Article Zlotnik A.A., Zlotnik I. A. Finite element method with discrete transparent boundary conditions for the one-dimensional nonstationary 1D Schrödinger equation / Пер. с рус. // Доклады Академии наук. 2012. Vol. 86. No. 3. P. 750-755. doi
- Article Zlotnik A., Zlotnik I. A. Finite element method with discrete transparent boundary conditions for the time-dependent 1D Schrödinger equation // Kinetic and Related Models. 2012. Vol. 5. No. 3. P. 639-667. doi
- Article Zlotnik A.A. Spatial discretization of one-dimensional quasi-gasdynamic systems of equations and the entropy and energy balance equations / Пер. с рус. // Доклады Академии наук. 2012. Vol. 86. No. 1. P. 464-468. doi
- Article Zlotnik A.A. Spatial discretization of the one-dimensional quasi-gasdynamic system of equations and the entropy balance equation / Пер. с рус. // Computational Mathematics and Mathematical Physics. 2012. Vol. 52. No. 7. P. 1060-1071. doi
20111
20104
- Article Zlotnik A. Linearized stability of equilibrium solutions to the quasi-gasdynamic system of equations / Пер. с рус. // Doklady Mathematics. 2010. Vol. 82. No. 2. P. 811-815. doi
- Article Zlotnik A. Quasi-gasdynamic system of equations with general equations of state / Пер. с рус. // Doklady Mathematics. 2010. Vol. 81. No. 2. P. 312-316. doi
- Article Zlotnik A., Lapukhina A. Stability of a Numerov type finite–difference scheme with approximate transparent boundary conditions for the nonstationary Schrödinger equation on the half-axis / Пер. с рус. // Journal of Mathematical Sciences. 2010. Vol. 169. No. 1. P. 84-97. doi
- Article Zlotnik A. Stability of small perturbations for a modified two-dimensional quasi-gasdynamic model of traffic flows / Пер. с рус. // Mathematical Models and Computer Simulations. 2010. Vol. 2. No. 6. P. 776-781. doi
20094
- Article Zlotnik A., Kireeva O. Error bounds for FEM with generalized cubic splines // Computational Methods in Applied Mathematics. 2009. Vol. 9. No. 2. P. 203-218. doi
- Article Zlotnik Alexander, Ducomet B., Zlotnik I. On a family of finite-difference schemes with approximate transparent boundary conditions for a generalized 1D Schrödinger equation // Kinetic and Related Models. 2009. Vol. 2. No. 1. P. 151-179. doi
- Article Zlotnik A., Ducomet B., Goutte H., Berger J. On one semidiscrete Galerkin method for a generalized time-dependent 2D Schrödinger equation // Applied Mathematics Letters. 2009. No. 22. P. 252-257. doi
- Article Zlotnik A., Ducomet B., Goutte H., Berger J. On one version of a semidiscrete Galerkin method for PDE problems involving a 2D Hamiltonian operator // Communications in Mathematical Sciences. 2009. Vol. 7. No. 2. P. 247-295. doi
Conferences
- 2022
Всероссийская научная конференция «Теоретические основы конструирования численных алгоритмов и решение задач математической физики», посвященная памяти К.И. Бабенко -2022 (Пущино). Presentation: О параболическом и гиперболическом 2-го порядка возмущениях симметричной гиперболической системы 1-го порядка
- 2019
International Conference on Differential and Difference Equations and Applications 2019 (Lisbon). Presentation: L^2-dissipativity of explicit regularized and linearized finite-difference schemes on a non-uniform spatial mesh for the 1d gas dynamics equations
International Conference on Differential Equations 2019 (Leiden). Presentation: On the strong continuity on data in weaker norms of global weak solutions to 1D viscous compressible Navier-Stokes equations and an error of their two-scale homogenization
- 17th International Conference of Numerical Analysis and Applied Mathematics (Rodos). Presentation: On Aggregated Regularized Equations for Homogeneous Binary Gas Mixture Flows with Viscous Compressible Components
- 2018
23rd International Conference Mathematical Modelling and Analysis (Сигулда). Presentation: On numerical simulation of spiral-vortical structures in rotating gaseous disks
- 201722nd International Conference Mathematical Modelling and Analysis (Druskininkai). Presentation: Fast FFT-based solvers for higher order FEM on rectangular parallelepipeds for PDE
22nd International Conference Mathematical Modelling and Analysis (Druskininkai). Presentation: Weak conservativeness criterions for QGD-schemes for 1D gas dynamics equations
International Conference on Differential & Difference Equations and Applications 2017 (Lisbon). Presentation: On a barotropic quasi-hydrodynamic system of equations for the two-component mixture with a diffuse interface
- Sixth China-Russia Conference on Numerical Algebra and Applications (Москва). Presentation: On fast Fourier solvers for the tensor product high-order finite element method for a generalized Poisson equation
- International Conference on Computer Simulation in Physics and beyond (Москва). Presentation: Numerical methods with discrete transparent boundary conditions for solving the time-dependent Schrödinger equation in unbounded domains
- 2016
Mathematical Modelling and Analysis 2016 (Тарту). Presentation: Properties of the Numerov-Crank-Nicolson Scheme on a Non-Uniform Mesh for the 1D Time-Dependent Schrödinger Equation
Computational Methods in Applied Mathematics - 7 (Jyvaskyla). Presentation: On conservative spatial discretizations for quasi-gasdynamic systems of equations
XXI Всероссийская конференция "Теоретические основы и конструирование численных алгоритмов для решения задач математической физики", посвященная памяти К.И. Бабенко (Дюрсо). Presentation: Новая пространственная дискретизация многомерной квазигазодинамической системы уравнений со свойством неубывания полной энтропии
- 2015Numerical Methods for Optimal Control and Inverse Problems 2015 (Munich). Presentation: Error estimates for methods of solving the time-dependent Schrödinger equations in unbounded domains
SCICADE2015 (Потсдам). Presentation: On error estimates for some numerical methods with discrete TBC for the time-dependent Schrödinger equation
- 2014Numerical Methods for Optimal Control and Inverse Problems (Munich). Presentation: Sharp error estimates for splitting finite element methods of solving second order hyperbolic equations
- Sixth Conference on Finite Difference Methods: Theory and Applications (Lozenetz). Presentation: New Results on Numerical Methods with Discrete TBC for Solving the TD Schrödinger Equation in Unbounded Domains
- Mathematical Theory of Gases and Fluids and Related Applications (Seoul). Presentation: On the Lipschitz continuity on data of weak solutions to 1D viscous compressible heat-conducting gas equations and its applications
- International Congress of Mathematicians 2014 (Seoul). Presentation: Higher order numerical methods for solving the time-dependent Schrödinger equation in unbounded domains
- XX Всероссийская конференция «Теоретические основы и конструирование численных алгоритмов и решения задач математической физики», посвященная памяти К.И. Бабенко (Дюрсо). Presentation: Пространственная дискретизация одномерной квазигазодинамической системы уравнений с общими уравнениями состояния и уравнение баланса энтропии
6th International Conference on Computational Methods in Applied Mathematics (Strobl). Presentation: Error estimates for numerical methods with discrete transparent boundary conditions for the time-dependent Schrödinger equation in unbounded domains
- Актуальные проблемы математической физики (Москва). Presentation: Методы с расщеплением по потенциалу и дискретными ПГУ для численного решения нестационарного уравнения Шрёдингера в неограниченном параллелепипеде
- 2013Numerical Computations: Theory and Algorithms 2013 (Фалерна). Presentation: A New Space Discretization of the 1D Quasi-Gas Dynamic System of Equations and the Entropy Balance Equation
- The Mathematics of Finite Elements and Applications 2013 (Лондон). Presentation: FEM with discrete transparent boundary conditions for the Cauchy problem for the Schrödinger equation on the whole axis
ENUMATH 2013 (лозанна). Presentation: The Crank-Nicolson scheme with splitting and discrete transparent boundary conditions for the Schrodinger equation on an infinite strip
- SciCADE 2013 (Вальядолид). Presentation: Finite-difference schemes with splitting and discrete TBCs for the 2D Schrödinger equation in a strip
- 201217th International Conference on Mathematical Modelling and Analysis (Tallinn). Presentation: The space discretization of the 1d quasi-gas dynamic systems of equations and the entropy and energy balance equations
- 5th Conference on Computational Methods in Applied Mathematics (Берлин). Presentation: The space discretization of the 1d quasi-gas dynamic systems of equations and the entropy and energy balance equations
Academic Supervision
1. Lomonosov Timofey Aleksandrovich. Dissipativity analysis of explicit linearized finite-difference methods with regularization for gas dynamics equations. The dissertation of the Philosophy Doctor in Applied Mathematics. M.: NRU HSE, 2020.
2. Gavrilin Vladimir Alekseevich. Conservative discretizations of one-dimensional quasi-gas and quasi-hydrodynamic systems of equations. The dissertation of the candidate of physical and mathematical sciences, specialty 01.01.07 - computational mathematics. Moscow, MPEI, 2016.
3. Kireeva Olga Ilyinichna. Projection-grid methods for stationary and non-stationary equations of the 4th order with nonsmooth data. The dissertation of the candidate of physical and mathematical sciences, specialty 01.01.07 - computational mathematics. Moscow, MPEI, 2002.
4. Zaitseva Svetlana Borisovna. Sharp error estimates for locally one-dimensional and vector methods for solving the heat equation. The dissertation of the candidate of physical and mathematical sciences, specialty 01.01.07 - computational mathematics. Moscow, MPEI, 1999.
5. Nguyen Zha Bao. Questions of the qualitative theory of equations of one-dimensional motion of a viscous gas in the presence of free boundaries. The dissertation of the candidate of physical and mathematical sciences, specialty 01.01.02 - differential equations. Moscow, 1998.
Editorial board membership
2021: Member of the Editorial Board, Entropy.
2020: Member of the Editorial Board, Symmetry.
2008–2022: Member of the Editorial Board, Mathematical Modeling and Analysis (Mathematical Modelling and Analysis).
2002–2015: Member of the Editorial Board, Computational Methods in Applied Mathematics.
Grants
Participation in RFBR and RSF projects in 2009-2024.
23-21-00061 RSF Construction and analysis of higher-accuracy numerical methods for solving some problems of wave physics (head)
22-11-00126 RSF Parallel algorithms and programs, coupled problems of heat and mass transfer, nonlinear processes on the surface, multiscale algorithms, continuum mechanics, molecular dynamics, high-speed aircraft
19-11-00169 RSF “Development and application of parallel quasi-gas and quasi-hydrodynamic algorithms and technologies” for 2019-2021 (main performer).
19-11-00104 RSF “New approaches to the development of algorithms for solving problems of continuum mechanics for ultra-high-performance computing systems” for 2019-2021.
19-01-00262 “Quasi-gasdynamic algorithms on modern computing platforms and modeling of actual problems of gas and hydrodynamics” for 2019-2021.
18-01-00587 “Theoretical research and application of a quasi-gasdynamic system of equations for solving problems of gas and hydrodynamics” for 2018-2020.
16-01-00048 "Development and new applications of quasi-gasdynamic numerical methods" for 2016-2018 (head)
14-11-00549 RSF "Development of a quasi-hydrodynamic approach for mathematical modeling of multiphase flows using supercomputers" in 2016.
13-01-00703 “Development and improvement of quasi-gasdynamic methods and their applications” for 2013-2015 (head).
14-01-90009-Bel-a "Development and study of grid algorithms for efficient calculations of some evolutionary problems of mathematical physics, hydrodynamics and dynamics of traffic flows" for 2014-2015.
12-01-90008-Bel_a “Development, analysis and application of new effective difference methods for solving multidimensional filtration and convection-diffusion problems” for 2012-2013.
10-01-90005-Bel_a “Development and research of effective grid algorithms and mathematical modeling of some problems of hydro- and gasdynamics” for 2010-2011.
10-01-00136-a “Development and applications of quasi-gas and quasi-hydrodynamic systems of equations” for 2010-2012.
09-01-12166-ofi_m “Asymptotic methods in some problems of mechanics of viscous compressible media and heat transfer by radiation” for 2009-2010 (co-head).
Employment history
2011 - present time: HSE University, Faculty of Economic Sciences, Department of Mathematics, 2011-2020 professor, since 2020 professor-researcher
2019- present time: Keldysh Institute of Applied Mathematics of the RAS, leading researcher (part-time)
Research and lecturing abroad
- Ecole Normale Superieure Assia Djebar of Constantine, Algerie, October-November, 2017
- Tianjin University of Finance and Economics, P.R. China, April-May, 2017
- Technische Universität München, Germany, February 2014, March 2015
- Centre de recherche scientifique du Commissariat à l'énergie atomique et aux énergies alternatives, Département de Physique Théorique et Appliquée, Ile-de-France, 2002-2007 and 2009-2012
- Zhejiang University, Hangzhou, P.R. China, August 2008
- Institute of Applied Physics and Computational Mathematics, Beijing, P.R. China, December 2001
- Università di Torino, Facoltà di Matematica “Giuseppe Peano”, Torino, Italy, October 2001
- Université Paris 7 Denis Didro, Paris, France, April 2001
- Institute of Mathematics, Czech Academy of Sciences, Prague, September 2000-January 2001 and July-August 2001
- Université Paris 6 Pierre et Marie Curie, Paris, France, March 2000
- Institut Mittag-Leffler of the Royal Swedish Academy of Sciences, Stockholm, May 1998
Membership in dissertation councils
Member of the Council for the review of dissertations for the scientific degrees
Candidate of Science and Doctor of Science in the specialties 01.01.02 "Differential Equations, Dynamical Systems and Optimal Control (Physics and Mathematics), 01.01.07" Computational Mathematics "(Physics and Mathematics) at National Research University "Moscow Power Engineering Institute"
Reviewer of papers for scientific journals:
Applicable Analysis, Applied Mathematics and Computation, Applied Numerical Mathematics, Boundary Value Problems, Computer Physics Communications, Computers and Fluids, Computers and Mathematics with Applications, Computational Methods in Applied Mathematics, Discrete and Continuous Dynamical Systems – A, Entropy, Journal of Computational and Applied Mathematics, Journal of Computational Physics, Journal of Differential Equations, Journal of Dynamical and Control Systems, Journal of Function Spaces, Journal of Mathematical Physics, Lithuanian Mathematical Journal, Mathematical Methods in the Applied Sciences, Mathematical Modelling and Analysis, Mathematics (Switzerland), Mathematics and Computers in Simulation, Methods and Applications of Analysis, Nonlinearity, Numerical Algorithms, Numerical Methods for Partial Differential Equations, The Royal Society of Edinburgh: Proceedings A, Russian Journal on Numerical Analysis and Mathematical Modelling, SIAM Journal on Mathematical Analysis, SIAM Journal of Numerical Analysis, Symmetry, Zeitschrift für angewandte Mathematik und Physik (ZAMP), Zeitschrift für Naturforschung A (A Journal of Physical Sciences)
and
Differential Equations, Computational Mathematics and Mathematical Physics, Izvestiya: Mathematics, Russian Mathematics (Iz. VUZ), Mathematical Notes, Mathematical Models and Computer Simulation, Numerical analysis and Applications, Proceedings of Institute for System Programming of the Russian Academy of Sciences, The HSE Economic Journal