mathematical modeling, variational and free boundary problems, numerical methods;
granular mechanics and aeolian sand transport, applied superconductivity, optimal transportation.
Publications and preprints:
o Sokolovsky V., Prigozhin L. and Barrett J. W. 3D modeling of magnetic atom traps on type-II superconductor chips. [pdf] Supercond. Science and Technology, 2014, v. 27, 124004.
o Barrett J. W. and Prigozhin L. Sandpiles and superconductors: Nonconforming linear finite element approximations for mixed formulations of quasi-variational inequalities. [pdf] IMA J. of Numerical Analysis, accepted.
o Barrett J. W. and Prigozhin L. Existence and approximation of a mixed formulation for thin film magnetization problems in superconductivity. [pdf] Mathematical Models and Methods in Applied Sciences (M3AS), 2014, v. 24, pp. 991-1015.
o Barrett J. W. and Prigozhin L. Lakes and rivers in the landscape: A quasi-variational inequality approach. [pdf] Interfaces and Free Boundaries, 2014, v. 16, 269-296.
o Barrett J. W., Prigozhin L. and Sokolovsky V. Transport current and magnetization problems for thin type-II superconducting films. [pdf] Supercond. Science and Technology, 2013, v. 26, 105009.
o Barrett J. W. and Prigozhin L. A quasi-variational inequality problem arising in the modeling of growing sandpiles. [pdf] ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 2013, v. 47, pp. 1133-1165.
o Spektor M., Meerovich V., Sokolovsky V. and Prigozhin L. AC losses in thin coated conductors under non-sinusoidal conditions. [pdf] Supercond. Science and Technology, 2012, v. 25, 025008.
o Prigozhin L. and Sokolovsky V. Computing AC losses in stacks of high-temperature superconducting tapes. [pdf], Supercond. Science and Technology, 2011, v. 24, 075012.
o Sokolovsky V., Prigozhin L., Dikovsky V. Meissner transport current in flat films of arbitrary shape and a magnetic trap for cold atoms. [pdf] Supercond. Science and Technology, 2010, v. 23, 065003.
o Barrett J. W. and Prigozhin L. A quasi-variational inequality problem in superconductivity. [pdf] Mathematical Models and Methods in Applied Sciences (M3AS), 2010, v. 20, 679-706.
o Manukyan E. and Prigozhin L. Formation of aeolian ripples and sand sorting. [pdf] Phys. Rev. E , 2009, v. 79, art. no. 031303.
o Barrett J. W. and Prigozhin L. Partial L1 Monge-Kantorovich problem: Variational formulation and numerical approximation. [ps] Interfaces and Free Boundaries, 2009, v. 11, pp. 201-238.
o Barrett J. W. and Prigozhin L. A mixed formulation of the Monge-Kantorovich equations. [pdf] ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), 2007, v. 41, pp. 1041-1060.
o Barrett J. W. and Prigozhin L. Dual formulations in critical-state problems. [pdf] Interfaces and Free Boundaries, 2006, v. 8, pp. 347-368.
o Barrett J. W. and Prigozhin L. Sandpiles and superconductors: dual formulations for critical-state problems [pdf], 2006, in: International Federation for Information Processing, v. 202, "Systems, Control, Modeling and Optimization", eds. Ceragioli, F., Dontchev, A., Furuta, H., Marti, K, Pandolfi, L. (Boston: Springer), pp. 25-29.
o Meerovich V., Sokolovsky V., Prigozhin L., Rozman D. Dynamic response of HTS composite tapes to pulsed currents. [pdf] Supercond. Science and Technology, 2006, v. 19, pp. 267-275.
o Prigozhin L. Solutions to Monge-Kantorovich equations as stationary points of a dynamical system, 2005. arXiv:math.OC/0507330 [pdf].
o Sokolovsky V., Prigozhin L. and Meerovich V. Penetration of spatially nonuniform alternating magnetic field into type-II superconductors. [pdf] Physica C, 2004, v. 408-410, pp. 645-646.
o Prigozhin L. and Sokolovsky V. AC losses in type-II superconductors induced by nonuniform fluctuations of external magnetic field. [pdf] IEEE Trans. on Applied Superconductivity, 2004, v. 14, pp. 69-81.
o Prigozhin L. Variational inequalities in critical-state problems. [pdf]. Physica D, 2004, v. 167, pp. 197-210.
o Prigozhin L. and Zaltzman B. On the approximation of the dynamics of sandpile surfaces. [pdf] Portugaliae Mathematica, 2003, v.60, n.2.
o Swartz J.P, McCulloch M.D., Pecher R., Prigozhin L., Vanderbemden Ph., Chapman S.J. Critical state modeling of crossed field demagnetization in HTS materials. [pdf] in: Applied Superconductivity 2003 (Proceedings of 6th EUCAS, Eds. Adreone A.et al., 2003), pp. 859-866.
o Prigozhin L. and Zaltzman B. Two continuous models for the dynamics of sandpile surfaces. [pdf] Phys. Rev. E., 2001, v. 63, art. no. 041505.
o Barrett J. W. and Prigozhin L. Bean's model as the p --> infinity limit of evolutionary p-Laplacian equations. [ps] Nonlinear Analysis, 2000, v. 42, pp. 977-993.
o Prigozhin L. Nonlinear dynamics of Aeolian sand ripples. [pdf] Phys. Rev. E, 1999, v. 60, pp. 729-733.
o Prigozhin L. Solution of thin film magnetization problems in superconductivity. [pdf] J. Comp. Phys., 1998, v. 144, pp. 180-193.
o Prigozhin L. and Kalman H. Radial mixing and segregation of a binary mixture in a rotating drum: Model and experiment. [pdf] Phys. Rev. E, 1998, v. 57, pp. 2073-2080.
o Prigozhin L. Analysis of critical state problems in type-II superconductivity. [pdf] IEEE Trans. on Applied Superconductivity, 1997, v. 7, No. 4, pp. 3866 - 3873.
o Prigozhin L. The Bean model in superconductivity: Variational formulation and numerical solution.[pdf] J. Comp. Phys., 1996, v. 129, 190-200.
o Prigozhin L. On the Bean critical-state model in superconductivity. [pdf] Euro. J. Appl. Math., 1996, v. 7, pp. 237-248.
o Prigozhin L. Variational model of sandpile growth. [pdf] Euro. J. Appl. Math., 1996, v. 7, pp. 225-236.
o Prigozhin L. Sandpiles, river networks, and type-II superconductors. [pdf] Free Boundary Problems News, 1996, No. 10, pp. 2-4.
o Prigozhin L. Sandpiles and river networks: extended systems with non-local interactions. [pdf] Phys. Rev. E, 1994, v. 49, pp. 1161-1167.
o Prigozhin L. A variational problem of bulk solids mechanics and free-surface segregation. [pdf] Chemical Engineering Science, 1993, v. 48, pp. 3647 - 3656.
o Mochalov I.A. and Prigozhin L. B. Variational problem of measurements optimization in identification and control algorithms. Kibernetika, 1987, No. 9, pp. 498-514.
o Kazakevich V.V., Mochalov I.A., and Prigozhin L.B. Measurements optimization for accelerated algorithms of extremum seeking in control systems. Avtomatika i Telemekhanika, 1986, No.9, pp. 60-69.
o Prigozhin L.B. Quasivariational inequality describing the shape of a poured pile. [pdf] Zhurnal Vichislitel'noy Matematiki i Matematicheskoy Fiziki, 1986, No.7, pp. 1072-1080.
o Prigozhin L.B. and Zolotarev P.P. On non-stationary stage of binary solution evaporation into vacuum. Zhurnal Fizicheskoy Khimii, 1986, v.60, pp. 690-692.
o Prigozhin L.B. and Zolotarev P.P. Finite element solution of adsorption problem with a singularity on the free boundary. Chislenniye Metodi Mekhaniki Sploshnoy Sredi, 1984, v.15, No.3, pp. 125-136.
o Prigozhin L.B. Solute dispersion in a pulsating fluid flow. [pdf] Proceedings of Academia of Science, USSR, ser. Mekhanika Zhidkosti i Gaza, 1982, No.5, pp. 24-30.
o Prigozhin L.B. and Bulgach A.A. Numerical solution of one-dimensional Stefan problems in heat conduction and diffusion. Chislenniye Metodi Mekhaniki Sploshnoy Sredi, 1981, v.12, No. 2, pp. 71-83.
o Prigozhin L.B. and Tolkachev V.M. Computation of glass sheet deformations at bending. - Prikladniye Problemi Prochnosti i Plastichnosti, 1977, No.7, pp. 109-116.
o Prigozhin L.B. Solution of heat balance equations for multipass heat exchangers. - Inzhenerno-Phizicheskiy Zhurnal, 1977, v. 32, No. 3, pp. 543-544.
o Poltavtseva L.L. and Prigozhin L.B. Computer simulation of heat exchangers. - Montazh i Naladka Sredstv Avtomatizatsii i Sviazi, 1976, ser. 8, No. 2(88), pp. 15-20.