Systems of conservation laws, qualitative properties and singularities of generalized solutions, variational representation of solutions. Systems of equations of multicomponent filtration type.
Main publications:
Yu. G. Rykov, “O kharaktere rasprostraneniya vozmuschenii dlya suschestvenno neavtonomnykh kvazilineinykh uravnenii pervogo poryadka.”, Trudy seminara im. I. G. Petrovskogo, 17, 1994, 89–117
W. E., Yu. G. Rykov, Ya. G. Sinai, “Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics”, Comm. Math. Phys., 177 (1996), 349–380
Yu. G. Rykov, “Discontinuous solutions of some strongly degenerate parabolic equations.”, Russian Journal of Mathematical Physics, 7:3 (2000), 341–356
Yu. G. Rykov, “On the non-hamiltonian character of shocks in 2-D pressureless gas.”, Bolletino dell U.M.I. Sezione B, 5-B (2002), 55–78
A. I. Aptekarev, Yu. G. Rykov, “On the variational representation of solutions to some quasilinear equations and systems of hyperbolic type on the basis of potential theory”, Russian Journal of Math. Phys., 13:1 (2006), 4–12
Yu. G. Rykov, “On the evolution of the hierarchy of shock waves in a two-dimensional isobaric medium”, Izv. RAN. Ser. Mat., 88:2 (2024), 96–126; Izv. Math., 88:2 (2024), 284–312
2023
2.
V. E. Borisov, V. T. Zhukov, M. M. Krasnov, B. V. Kritskiy, N. D. Novikova, Yu. G. Rykov, O. B. Feodoritova, “Program package NOISEtte-MCFL for simulation multicomponent reacting flows”, Keldysh Institute preprints, 2023, 006, 23 pp.
V. I. Baluta, V. P. Osipov, Yu. G. Rykov, B. N. Chetverushkin, “On the concept of influence in the concept of cognitive modeling when using the activation function of the ReLU type”, Informatsionnye Tekhnologii i Vychslitel'nye Sistemy, 2023, no. 4, 59–71
N. V. Klyushnev, Yu. G. Rykov, “On model two-dimensional pressureless gas flows: Variational description and numerical algorithm based on adhesion dynamics”, Zh. Vychisl. Mat. Mat. Fiz., 63:4 (2023), 639–656; Comput. Math. Math. Phys., 63:4 (2023), 606–622
Yu. G. Rykov, “On modeling the development of the region in conditions of high uncertainty and lack of data”, Keldysh Institute preprints, 2022, 034, 16 pp.
7.
V. E. Borisov, B. V. Kritsky, Yu. G. Rykov, “MCFL-Chem software module for numerical simulation of high-speed reacting flows”, Keldysh Institute preprints, 2022, 021, 40 pp.
E. Yu. Akulinina, A. L. Karmanov, N. A. Teplykh, V. V. Vlasov, V. I. Baluta, S. S. Varykhanov, A. A. Karandeev, V. P. Osipov, Yu. G. Rykov, B. N. Chetverushkin, “Extracting factual information about the pandemic from open Internet sources”, Mat. Biolog. Bioinform., 17:2 (2022), 423–440
9.
A. I. Aptekarev, Yu. G. Rykov, “Emergence of a Hierarchy of Singularities in Zero-Pressure Media. Two-Dimensional Case”, Mat. Zametki, 112:4 (2022), 486–499; Math. Notes, 112:4 (2022), 495–504
V. P. Osipov, Yu. G. Rykov, B. N. Chetverushkin, “Mathematical aspects of the concept of influence in the cognitive simulations”, Artificial Intelligence and Decision Making, 2021, no. 2, 3–10; Scientific and Technical Information Processing, 49:5 (2022), 350–355
11.
Yu. G. Rykov, “The technology of using fuzzy cognitive maps from a mathematical point of view”, Keldysh Institute preprints, 2021, 073, 22 pp.
Yu. G. Rykov, “Variational Formulation of the Problem of Finding Generalized Solutions for Quasilinear Hyperbolic Systems of Conservation Laws”, Mat. Zametki, 110:6 (2021), 944–947; Math. Notes, 110:6 (2021), 972–975
2020
13.
V. E. Borisov, Yu. G. Rykov, “Simulation of multicomponent gas flows using double-flux method”, Matem. Mod., 32:10 (2020), 3–20; Math. Models Comput. Simul., 13:3 (2021), 453–465
A. I. Aptekarev, Yu. G. Rykov, “Detailed description of the evolution mechanism for singularities in the system of pressureless gas dynamics”, Dokl. Akad. Nauk, 484:6 (2019), 7–10; Dokl. Math., 99:1 (2019), 79–82
V. T. Zhukov, Yu. G. Rykov, O. B. Feodoritova, “Mathematical model of multicomponent mixture flow of gases with regard to the possibility of the liquid phase”, Keldysh Institute preprints, 2018, 183, 36 pp.
V. E. Borisov, Yu. G. Rykov, “An exact Riemann solver in the algorithms for multicomponent gas dynamics”, Keldysh Institute preprints, 2018, 096, 28 pp.
Yu. G. Rykov, “Multi-D variational principle and pressureless gas dynamics”, Keldysh Institute preprints, 2018, 080, 12 pp.
20.
V. A. Bakhtin, I. P. Bogdanov, V. P. Osipov, Yu. G. Rykov, A. A. Smirnov, V. A. Sudakov, “Optimal scheduling of homogeneous products transportation”, Keldysh Institute preprints, 2018, 065, 26 pp.
Yu. G. Rykov, “On the variational approach to systems of quasilinear conservation laws”, Trudy Mat. Inst. Steklova, 301 (2018), 225–240; Proc. Steklov Inst. Math., 301 (2018), 213–227
E. V. Borovik, M. M. Krasnov, Yu. G. Rykov, D. K. Shalyga, “The mathematical model and numerical approach based on ENO schemes for the flows in variable cross-section channels with combustion”, Keldysh Institute preprints, 2016, 112, 20 pp.
23.
Yu. G. Rykov, “2D pressureless gas dynamics and variational principle”, Keldysh Institute preprints, 2016, 094, 14 pp.
A. A. Ilyin, Yu. G. Rykov, “On the closeness of trajectories for model quasi-gasdynamic equations. Linear case”, Keldysh Institute preprints, 2016, 090, 14 pp.
E. V. Borovik, A. V. Goncharov, Yu. G. Rykov, D. N. Tulyakov, “On the calculation of 2D compressible filtration flows by the ‘compressible streamlines’ methodology”, Keldysh Institute preprints, 2016, 064, 12 pp.
26.
I. G. Gudich, V. T. Zhukov, K. V. Manukovskii, N. D. Novikova, Yu. G. Rykov, O. B. Feodoritova, “Numerical simulation of high-speed combustion chamber by OpenFOAM”, Keldysh Institute preprints, 2016, 010, 32 pp.
V. T. Zhukov, K. V. Manukovskii, N. D. Novikova, Yu. G. Rykov, O. B. Feodoritova, “On high velocity flow simulation in model ramjet engine”, Keldysh Institute preprints, 2015, 005, 23 pp.
V. G. Lysov, Yu. G. Rykov, “On the computation of the phase equilibrium in multicomponent filtration problems”, Keldysh Institute preprints, 2014, 094, 20 pp.
N. A. Zaitsev, B. V. Kritskii, Yu. G. Rykov, “On a two-dimensional model for computations of two-phase flows”, Keldysh Institute preprints, 2014, 086, 32 pp.
Yu. G. Rykov, O. B. Feodoritova, “On the methodology of variational representation of generalized solutions to quasi-linear hyperbolic two-equations systems”, Keldysh Institute preprints, 2014, 084, 22 pp.
A. A. Ilyin, Yu. G. Rykov, “On a model system with a small parameter as a coefficient of the highest time derivative arising in the analysis of certain quasihydrodymamical systems”, Keldysh Institute preprints, 2012, 075, 9 pp.
Yu. G. Rykov, V. G. Lysov, O. B. Feodoritova, “The emergence of non-classic shocks in a flow model of two-component, two-velocity medium”, Keldysh Institute preprints, 2012, 074, 20 pp.
34.
V. M. Goloviznin, N. A. Zaitsev, V. V. Kabanov, V. G. Lysov, Yu. G. Rykov, “On some approach to direct numerical simulation of two-phase flows”, Keldysh Institute preprints, 2012, 073, 36 pp.
Yu. G. Rykov, N. A. Zaitsev, V. V. Kabanov, V. G. Lysov, R. F. Khabibullin, “Possible thermodynamic model for the usage in the schematics of DNS for two-phase flows”, Keldysh Institute preprints, 2012, 040, 18 pp.
A. A. Ilyin, Yu. G. Rykov, “On a model equation with small parameter as a coefficient of the second-order time derivative arising in the analysis of certain quasi-gasdynamics systems”, Keldysh Institute preprints, 2012, 012, 9 pp.
V. T. Zhukov, N. A. Zaitsev, V. G. Lysov, Yu. G. Rykov, O. B. Feodoritova, “Numerical analysis of new model of metals cristallization processes, two-dimensional case”, Matem. Mod., 24:1 (2012), 109–128; Math. Models Comput. Simul., 4:4 (2012), 440–453
Yu. G. Rykov, “A variational representation of generalized solutions to quasi-linear hyperbolic systems and possible algorithms for hybrid supercomputers”, Keldysh Institute preprints, 2011, 062, 9 pp.
Yu. G. Rykov, “On the Generalization of Conservation Law Theory to Certain Degenerate Parabolic Systems of Equations Describing Processes of Compressible Two-Phase Multicomponent Filtration”, Mat. Zametki, 89:2 (2011), 300–315; Math. Notes, 89:2 (2011), 291–303
Elena Koldoba, Alexander Koldoba, Artyom Myasnikov, Olga Podgornova, Yuri Rykov, “Thermodynamically consistent approach for numerical simulation of oil displacement processes”, Matem. Mod., 21:10 (2009), 7–18
Yu. G. Rykov, “A rigorous formulation of streamline approach in reservoir simulation for compressible compositional case”, Keldysh Institute preprints, 2008, 004, 16 pp.
N. A. Zaitsev, Yu. G. Rykov, “The numerical calculation of some model, which describes the metals’ crystallization process I. 1-D case”, Keldysh Institute preprints, 2007, 072, 16 pp.
44.
Yu. G. Rykov, “On the Riemann problem for the system of equations of two-component, two-phase filtration in porous media in case of both phases compressibility”, Keldysh Institute preprints, 2007, 059, 16 pp.
N. A. Zaitsev, Yu. B. Radvogin, Yu. G. Rykov, “Computation of non-stationary swirled flows in nozzles and pipes using new ‘explicit-implicit’ type scheme”, Keldysh Institute preprints, 2004, 052, 32 pp.
Yu. G. Rykov, “On the Generalization of Burgers Equation to the Case of Linebreak Bounded Dissipation Flux”, Keldysh Institute preprints, 1999, 050
47.
Yu. G. Rykov, “Propagation of singularities of shock wave type in a system of equations of two-dimensional pressureless gas dynamics”, Mat. Zametki, 66:5 (1999), 760–769; Math. Notes, 66:5 (1999), 628–635
Yu. G. Rykov, “The Singularities of Type of Shock Waves in Pressureless Medium, the Solutions in the Sense of Measures and Kolombo's Sense”, Keldysh Institute preprints, 1998, 030
Yu. G. Rykov, “On the Dynamical System which Corresponds To 2-D System of Gas Dynamics without Pressure”, Keldysh Institute preprints, 1997, 068
1996
50.
Yu. G. Rykov, “The Cauchy problem for some models of one-dimensional gas
dynamics”, Dokl. Akad. Nauk, 349:6 (1996), 740–742
51.
Yu. G. Rykov, “The Numerical Method for Solving the 2-D System of Gas Dynamics without Pressure”, Keldysh Institute preprints, 1996, 076
52.
Yu. G. Rykov, “A variational principle for a two-dimensional system of equations of gas dynamics without stress”, Uspekhi Mat. Nauk, 51:1(307) (1996), 165–166; Russian Math. Surveys, 51:1 (1996), 162–164
Yu. G. Rykov, “The Existence Theorems for Cauchy Problem to One Dimensional Models of Gas Dynamics”, Keldysh Institute preprints, 1995, 107
54.
I. Veinan, Yu. G. Rykov, Ya. G. Sinai, “The Lax–Oleinik variational principle for some one-dimensional systems of quasilinear equations”, Uspekhi Mat. Nauk, 50:1(301) (1995), 193–194; Russian Math. Surveys, 50:1 (1995), 220–222
Yu. G. Rykov, “Localization of perturbations in a boundary value problem for a first-order quasilinear equation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1988, no. 1, 73–75
1987
56.
Yu. G. Rykov, “Character of propagation of disturbances in the Cauchy problem for quasilinear first-order equations”, Mat. Zametki, 42:5 (1987), 712–722; Math. Notes, 42:5 (1987), 892–897
The interaction of shocks in 2D pressureless medium Yu. G. Rykov III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 7, 2023 10:00
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