[Текст] : статья / I.I. Ryzhkov // Lournal of Applied Mechanics and Technical Physics. - 2011. - Vol. 52, Iss. 4. - p. 560-570DOI 10.1134/S0021894411040080
. -
Аннотация: A model of vibrational convection of a binary mixture with the thermodiffusion effect is considered. The symmetries of model equations are found, depending on the values of physical parameters. A partially invariant solution, which describes separation of the binary mixture in a thermodiffusion column, is constructed and studied. The influence of streamwise vibrations on the flow regime and separation of the mixture is investigated.
Полный текст на сайте правообладателя
Доп.точки доступа:
Stepanova, I.V.; Степанова, Ирина Владимировна; Рыжков, Илья Игоревич
Труды сотрудников ИВМ СО РАН
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Group properties and exact solutions of equations for vibrational convection of a binary mixture
Symmetries of equations for vibrational convection in binary mixture
[Text] : статья / I. V. Stepanova, I. I. Ryzhkov // Proceedings of 5-th Int. Workshop in Group analysis of differential equations and integrable system. - 2011. - p. 200-206
. - ISBN 978-9963-700-07-3
Аннотация: Dust kinetic Alfven waves (DKAW) instability with Kappa-distributed ions streaming effects have been examined rigorously in a uniform dusty magnetoplasma. A dispersion relation of low-frequency DKAW instability on the dust acoustic velocity branch is obtained in a low-beta Lorentzian plasma. It is found that nonthermality is more effective for dust kinetic Alfven waves in the perpendicular component having finite larmor radius effects. Lorentzian type charging currents are obtained with the aid of Vlasov theory. Effect of different dust parameters on the growth rates of instability are considered. Damping/instability due to dust charge fluctuation is found to be insensitive to the form of the distribution function for DKAW. Possible applications to dusty space plasmas are pointed out.
Сборник трудов на сайте издательства
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Ryzhkov, I.I.; Рыжков, Илья Игоревич; Степанова, Ирина Владимировна; International Workshop in Group analysis of differential equations and integrable system(5 ; June 6–10, 2010 ; Protaras)
Аннотация: Dust kinetic Alfven waves (DKAW) instability with Kappa-distributed ions streaming effects have been examined rigorously in a uniform dusty magnetoplasma. A dispersion relation of low-frequency DKAW instability on the dust acoustic velocity branch is obtained in a low-beta Lorentzian plasma. It is found that nonthermality is more effective for dust kinetic Alfven waves in the perpendicular component having finite larmor radius effects. Lorentzian type charging currents are obtained with the aid of Vlasov theory. Effect of different dust parameters on the growth rates of instability are considered. Damping/instability due to dust charge fluctuation is found to be insensitive to the form of the distribution function for DKAW. Possible applications to dusty space plasmas are pointed out.
Сборник трудов на сайте издательства
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Ryzhkov, I.I.; Рыжков, Илья Игоревич; Степанова, Ирина Владимировна; International Workshop in Group analysis of differential equations and integrable system(5 ; June 6–10, 2010 ; Protaras)
Symmetries of Euler equations in Lagrangian coordinates
/ V. Andreev // Journal of Nonlinear Mathematical Physics. - 1996. - Vol. 3, Is. 1-2. - P196-201
. - ISSN 1402-9251
Аннотация: The transition from Eulerian to Lagrangian coordinates is a nonlocal transformation. In general, isomorphism should not take place between basic Lie groups of studied equations. Besides, in the case of plane and rotational symmetric motion hydrodynamic equations in Lagrangian coordinates are partially integrated. This fact introduces arbitrary functions, initial data, to the resulting systems and makes cuurently central the problem of group classification. It is stated that under a transition to Lagrangian coordinates, the main group becomes infinite-dimensional as well in space coordinates. The exclusive values of arbitrary functions of Lagrange coordinates (vorticity, momentum), at which the further group widening takes place, are found in [1]. Copyright В© 1996 by Mathematical Ukraina Publisher. All rights of reproduction in any form reserved.
Scopus
Держатели документа:
Computing Center, SB of the Russian Academy of Sciences, Krasnoyarsk, 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Andreev, V.K.; Андреев, Виктор Константинович
Аннотация: The transition from Eulerian to Lagrangian coordinates is a nonlocal transformation. In general, isomorphism should not take place between basic Lie groups of studied equations. Besides, in the case of plane and rotational symmetric motion hydrodynamic equations in Lagrangian coordinates are partially integrated. This fact introduces arbitrary functions, initial data, to the resulting systems and makes cuurently central the problem of group classification. It is stated that under a transition to Lagrangian coordinates, the main group becomes infinite-dimensional as well in space coordinates. The exclusive values of arbitrary functions of Lagrange coordinates (vorticity, momentum), at which the further group widening takes place, are found in [1]. Copyright В© 1996 by Mathematical Ukraina Publisher. All rights of reproduction in any form reserved.
Scopus
Держатели документа:
Computing Center, SB of the Russian Academy of Sciences, Krasnoyarsk, 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Andreev, V.K.; Андреев, Виктор Константинович
International symmetries of lattice hydrodynamics
[Text] / S. . Succi, H. . Chen, I. . Karlin // J. Phys. IV. - 1998. - Vol. 8: Conference on Disorder and Chaos in Honour and Memory of Giovanni Paladin (SEP 22-24, 1997, ROME, ITALY), Is. P6. - P271-275, DOI 10.1051/jp4:1998637. - Cited References: 11
. - ISSN 1155-4339
РУБ Physics, Multidisciplinary
Аннотация: We discuss some internal symmetries of lattice hydrodynamics and point out possible analogies with statistical field theory.
WOS
Держатели документа:
Ist Applicaz Calcolo, Rome, Italy
EXA Corp, Boston, MA USA
RAS, Ctr Comp, Krasnoyarsk, Russia
ИВМ СО РАН
Доп.точки доступа:
Succi, S.; Chen, H.; Karlin, I.; Карлин, Илья Вениаминович
Аннотация: We discuss some internal symmetries of lattice hydrodynamics and point out possible analogies with statistical field theory.
WOS
Держатели документа:
Ist Applicaz Calcolo, Rome, Italy
EXA Corp, Boston, MA USA
RAS, Ctr Comp, Krasnoyarsk, Russia
ИВМ СО РАН
Доп.точки доступа:
Succi, S.; Chen, H.; Karlin, I.; Карлин, Илья Вениаминович
Symmetry analysis of nonlinear heat and mass transfer equations under Soret effect
/ I. V. Stepanova // Comm. Nonlinear Sci. Numer. Simul. - 2015. - Vol. 20, Is. 3. - P684-691, DOI 10.1016/j.cnsns.2014.06.043
. - ISSN 1007-5704
Кл.слова (ненормированные):
Exact solutions -- Group classification problem -- Lie symmetry analysis -- Thermodiffusion equations -- Transport coefficients -- Exact solution -- Group classification -- Lie symmetry analysis -- Thermodiffusion -- Transport coefficient
Аннотация: Three-dimensional equations describing heat and mass transfer in fluid mixtures with variable transport coefficients are studied. Using Lie group theory the forms of unknown thermal diffusivity, diffusion and thermal diffusion coefficients are found. The symmetries of the governing equations are calculated. It is shown that cases of Lie symmetry extension arise when arbitrary elements have the power-law, logarithmic and exponential dependencies on temperature and concentration. An exact solution is constructed for the case of linear dependence of diffusion and thermodiffusion coefficients on temperature. The solution demonstrates differences in concentration distribution in comparison with the same distribution under constant transport coefficients in the governing equations. © 2014 Elsevier B.V.
Scopus
Держатели документа:
Institute of Computational Modeling SB RAS, 50/44, Krasnoyarsk, Akademgorodok, Russian Federation
Доп.точки доступа:
Stepanova, I. V.
Кл.слова (ненормированные):
Exact solutions -- Group classification problem -- Lie symmetry analysis -- Thermodiffusion equations -- Transport coefficients -- Exact solution -- Group classification -- Lie symmetry analysis -- Thermodiffusion -- Transport coefficient
Аннотация: Three-dimensional equations describing heat and mass transfer in fluid mixtures with variable transport coefficients are studied. Using Lie group theory the forms of unknown thermal diffusivity, diffusion and thermal diffusion coefficients are found. The symmetries of the governing equations are calculated. It is shown that cases of Lie symmetry extension arise when arbitrary elements have the power-law, logarithmic and exponential dependencies on temperature and concentration. An exact solution is constructed for the case of linear dependence of diffusion and thermodiffusion coefficients on temperature. The solution demonstrates differences in concentration distribution in comparison with the same distribution under constant transport coefficients in the governing equations. © 2014 Elsevier B.V.
Scopus
Держатели документа:
Institute of Computational Modeling SB RAS, 50/44, Krasnoyarsk, Akademgorodok, Russian Federation
Доп.точки доступа:
Stepanova, I. V.
Symmetry of Siberian Larch Transcriptome
[Text] : статья / Michael G. Sadovsky [et al.] // Журнал Сибирского федерального университета. Серия: Биология. - 2015. - Т. 8, № 3. - P278-286, DOI 10.17516/1997-1389-2015-8-3-278-286
. - ISSN 1997-1389
Перевод заглавия: Симметрия транскриптома сибирской лиственницы
Кл.слова (ненормированные):
Larix sibirica -- сложность -- nucleotide sequence complexity -- frequency dictionary -- order -- Siberian larch -- symmetry -- transcriptome -- triplet -- нуклеотидная последовательность -- частотный словарь -- порядок -- сибирская лиственница -- симметрия -- транскриптом -- триплет
Аннотация: The paper presents a novel approach to infer a structuredness in a set of symbol sequences such as transcriptome nucleotide sequences. A distribution pattern of triplet frequencies in the Siberian larch (Larix sibirica Ledeb.) transcriptome sequences was investigated in the presented study. It was found that the larch transcriptome demonstrates a number of unexpected symmetries in the statistical and combinatorial properties.
Проанализированы структуры, выделяемые в транскриптоме лиственницы. Показано, что данный набор последовательностей обладает необычной симметрией своих статистических и комбинаторных свойств.
РИНЦ
Держатели документа:
Georg-August-University of Gottingen
Institute of Computational Modelling SB RAS
M University HFSB
N. I. Vavilov Institute of General Genetics RAS
Siberian Federal University Genome Research and Education Centre
Texas A&
V. N. Sukachev Institute of Forest SB RAS
Доп.точки доступа:
Sadovsky, M.G.; Садовский, Михаил Георгиевич; Birukov, Vladislav V.; Бирюков В.В.; Putintseva, Yuliya A.; Путинцева Ю.А.; Oreshkova, Nataliya V.; Орешкова Н.В.; Vaganov, Eugene A.; Ваганов Е.А.; Krutovsky, Konstantin V.; Крутовский К.В.
Перевод заглавия: Симметрия транскриптома сибирской лиственницы
| УДК |
Кл.слова (ненормированные):
Larix sibirica -- сложность -- nucleotide sequence complexity -- frequency dictionary -- order -- Siberian larch -- symmetry -- transcriptome -- triplet -- нуклеотидная последовательность -- частотный словарь -- порядок -- сибирская лиственница -- симметрия -- транскриптом -- триплет
Аннотация: The paper presents a novel approach to infer a structuredness in a set of symbol sequences such as transcriptome nucleotide sequences. A distribution pattern of triplet frequencies in the Siberian larch (Larix sibirica Ledeb.) transcriptome sequences was investigated in the presented study. It was found that the larch transcriptome demonstrates a number of unexpected symmetries in the statistical and combinatorial properties.
Проанализированы структуры, выделяемые в транскриптоме лиственницы. Показано, что данный набор последовательностей обладает необычной симметрией своих статистических и комбинаторных свойств.
РИНЦ
Держатели документа:
Georg-August-University of Gottingen
Institute of Computational Modelling SB RAS
M University HFSB
N. I. Vavilov Institute of General Genetics RAS
Siberian Federal University Genome Research and Education Centre
Texas A&
V. N. Sukachev Institute of Forest SB RAS
Доп.точки доступа:
Sadovsky, M.G.; Садовский, Михаил Георгиевич; Birukov, Vladislav V.; Бирюков В.В.; Putintseva, Yuliya A.; Путинцева Ю.А.; Oreshkova, Nataliya V.; Орешкова Н.В.; Vaganov, Eugene A.; Ваганов Е.А.; Krutovsky, Konstantin V.; Крутовский К.В.
De novo assembly and cluster analysis of Siberian Larch transcriptome and genome
/ M. Sadovsky [et al.] // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2016. - Vol. 9656: 4th International Work-Conference on Bioinformatics and Biomedical Engineering, IWBBIO 2016; Granada; Spain; 20 April 2016 through 22 April 2016; Code 173369. - P455-464, DOI 10.1007/978-3-319-31744-1_41
. -
Кл.слова (ненормированные):
Cluster -- Elastic map -- Evolution -- Frequency -- Order -- Triplet -- Bioinformatics -- Biomedical engineering -- Genes -- Cluster -- Evolution -- Frequency -- Order -- Triplet -- Cluster analysis
Аннотация: We studied Siberian Larch (Larix Sibirica) transcriptome making de novo assembly and cluster analysis of contigs frequency dictionaries. Also, some preliminary results of similar study of the larch genome are present. It was found that the larch transcriptome yields a number of unexpected symmetries in the statistical and combinatorial properties of the entities. © Springer International Publishing Switzerland 2016.
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Смотреть статью,
WOS
Держатели документа:
Institute of Computational Modelling of SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Sadovsky, M.; Putintseva, Y.; Birukov, V.; Novikova, S.; Krutovsky, K.
Кл.слова (ненормированные):
Cluster -- Elastic map -- Evolution -- Frequency -- Order -- Triplet -- Bioinformatics -- Biomedical engineering -- Genes -- Cluster -- Evolution -- Frequency -- Order -- Triplet -- Cluster analysis
Аннотация: We studied Siberian Larch (Larix Sibirica) transcriptome making de novo assembly and cluster analysis of contigs frequency dictionaries. Also, some preliminary results of similar study of the larch genome are present. It was found that the larch transcriptome yields a number of unexpected symmetries in the statistical and combinatorial properties of the entities. © Springer International Publishing Switzerland 2016.
Scopus,
Смотреть статью,
WOS
Держатели документа:
Institute of Computational Modelling of SB RAS, Akademgorodok, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Sadovsky, M.; Putintseva, Y.; Birukov, V.; Novikova, S.; Krutovsky, K.
Редукции уравнений с частными производными к системам обыкновенных дифференциальных уравнений
[Текст] : статья / Олег Викторович Капцов, Дмитрий Олегович Капцов // Вычислительные технологии. - 2017. - Т. 22, № 4. - С. 61-68
. - ISSN 1560-7534
Перевод заглавия: Reduction of partial differential equations to the systems of ordinary differential equations
Кл.слова (ненормированные):
дифференциальные уравнения с частными производными -- обыкновенные дифференциальные уравнения -- инвариантные многообразия -- редукции уравнений -- partial differential equations -- systems of ordinary differential -- invariant manifolds -- the reduction of equations
Аннотация: Предложен метод использования симметрий высших порядков и инвapиaнтных мнoгоoбpaзий для поиска совместного численного решения уравнений с частными производными. Необходимость применения такого подхода обусловлена невозможностью нахождения общего решения подобных уравнений в большинстве случаев. Рассмотрены примеры использования предложенного подхода к уравнениям Кортевега -де Фриза, sin-Гордон и sh-Гордон с графиками решений.
In our article we develop an approach for constructing particular solutions of differential equations. This approach is based on the use of higher symmetries allowed by partial differential equations and the method of differential constraints proposed by N.N. Yanenko. We restrict ourselves to the study of partial differential equations with two independent variables. Differential constraints and the coefficients of admissible symmetry operators generate ordinary differential equations. The classical Lie theory works well in the case of point and contact transformations. When higher symmetries and higher-order differential constraints are considered then arises the problem of integrating higher-order ordinary differential equations. The solutions of such differential equations are obtained by the inverse scattering problem and finite-zone integration method in the soliton theory. However, this approach has a number of significant difficulties. For example, it is often difficult to sort out real solutions from a set of complex solutions, or solutions are expressed through insufficiently studied functions. Our approach is based on the numerical integration of passive systems. The additional ordinary differential equations are invariant manifolds of evolution equations. This allows us to rewrite an overdetermed system as two systems of ordinary differential equations. Further we sequentially solve these systems by the Runge -Kutta method. We apply this approach to the Korteweg - de Vries equations, Sin-Gordon and Sinh-Gordon equations. The bounded and unrestricted solutions are found and solution images are constructed. This approach can be used for equations with an arbitrary number of independent variables.
РИНЦ,
Полный текст (доступен только в ЛВС)
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Капцов, Олег Викторович; Kaptsov Oleg Viktorovich; Капцов, Дмитрий Олегович; Kaptsov Dmitry Olegovich
Перевод заглавия: Reduction of partial differential equations to the systems of ordinary differential equations
Кл.слова (ненормированные):
дифференциальные уравнения с частными производными -- обыкновенные дифференциальные уравнения -- инвариантные многообразия -- редукции уравнений -- partial differential equations -- systems of ordinary differential -- invariant manifolds -- the reduction of equations
Аннотация: Предложен метод использования симметрий высших порядков и инвapиaнтных мнoгоoбpaзий для поиска совместного численного решения уравнений с частными производными. Необходимость применения такого подхода обусловлена невозможностью нахождения общего решения подобных уравнений в большинстве случаев. Рассмотрены примеры использования предложенного подхода к уравнениям Кортевега -де Фриза, sin-Гордон и sh-Гордон с графиками решений.
In our article we develop an approach for constructing particular solutions of differential equations. This approach is based on the use of higher symmetries allowed by partial differential equations and the method of differential constraints proposed by N.N. Yanenko. We restrict ourselves to the study of partial differential equations with two independent variables. Differential constraints and the coefficients of admissible symmetry operators generate ordinary differential equations. The classical Lie theory works well in the case of point and contact transformations. When higher symmetries and higher-order differential constraints are considered then arises the problem of integrating higher-order ordinary differential equations. The solutions of such differential equations are obtained by the inverse scattering problem and finite-zone integration method in the soliton theory. However, this approach has a number of significant difficulties. For example, it is often difficult to sort out real solutions from a set of complex solutions, or solutions are expressed through insufficiently studied functions. Our approach is based on the numerical integration of passive systems. The additional ordinary differential equations are invariant manifolds of evolution equations. This allows us to rewrite an overdetermed system as two systems of ordinary differential equations. Further we sequentially solve these systems by the Runge -Kutta method. We apply this approach to the Korteweg - de Vries equations, Sin-Gordon and Sinh-Gordon equations. The bounded and unrestricted solutions are found and solution images are constructed. This approach can be used for equations with an arbitrary number of independent variables.
РИНЦ,
Полный текст (доступен только в ЛВС)
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Капцов, Олег Викторович; Kaptsov Oleg Viktorovich; Капцов, Дмитрий Олегович; Kaptsov Dmitry Olegovich
517.95
О-11
О-11
О ВЫСШИХ СИММЕТРИЯХ УРАВНЕНИЯ МУТАРА
[Текст] : статья / Ю. В. Шанько // Решетневские чтения. - 2018. - Т. 1, № 22. - С. 592-593
. - ISSN 1990-7702
Перевод заглавия: ON HIGHER SYMMETRIES OF MOUTARD EQUATION
Кл.слова (ненормированные):
уравнение Мутара -- высшие симметрии -- Moutard equation -- higher symmetries
Аннотация: Рассматриваются линейные высшие симметрии для уравнения Мутара.
Linear higher symmetries for Moutard equation are studied in this paper.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Шанько, Ю.В.; Shan'ko Yu. V.
Перевод заглавия: ON HIGHER SYMMETRIES OF MOUTARD EQUATION
| УДК |
Кл.слова (ненормированные):
уравнение Мутара -- высшие симметрии -- Moutard equation -- higher symmetries
Аннотация: Рассматриваются линейные высшие симметрии для уравнения Мутара.
Linear higher symmetries for Moutard equation are studied in this paper.
РИНЦ
Держатели документа:
Институт вычислительного моделирования СО РАН
Доп.точки доступа:
Шанько, Ю.В.; Shan'ko Yu. V.
Symmetries of Differential Ideals and Differential Equations
/ O. V. Kaptsov // J. Sib. Fed. Univ.-Math. Phys. - 2019. - Vol. 12, Is. 2. - P185-190, DOI 10.17516/1997-1397-2018-12-2-185-190. - Cited References:10. - The work was supported by the Russian Foundation for Basic Research (grant 17-01-00332-a).
. - ISSN 1997-1397. - ISSN 2313-6022
РУБ Mathematics
Аннотация: The paper deals with differential rings and partial differential equations with coefficients in some algebra. We introduce symmetries and the conservation laws to the differential ideal of an arbitrary differential ring. We prove that a set of symmetries of an ideal forms a Lie ring and give a precise criterion when a differentiation is a symmetry of an ideal. These concepts are applied to partial differential equations.
WOS,
Смотреть статью,
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РИНЦ
Держатели документа:
Inst Computat Modelling SD RAS, Acad Gorodok 50-44, Krasnoyarsk 660036, Russia.
Доп.точки доступа:
Kaptsov, Oleg, V; Russian Foundation for Basic Research [17-01-00332-a]
Аннотация: The paper deals with differential rings and partial differential equations with coefficients in some algebra. We introduce symmetries and the conservation laws to the differential ideal of an arbitrary differential ring. We prove that a set of symmetries of an ideal forms a Lie ring and give a precise criterion when a differentiation is a symmetry of an ideal. These concepts are applied to partial differential equations.
WOS,
Смотреть статью,
Scopus,
РИНЦ
Держатели документа:
Inst Computat Modelling SD RAS, Acad Gorodok 50-44, Krasnoyarsk 660036, Russia.
Доп.точки доступа:
Kaptsov, Oleg, V; Russian Foundation for Basic Research [17-01-00332-a]
532.5; 51-72
С 37
С 37
СИММЕТРИИ В УРАВНЕНИЯХ ТЕПЛОМАССОПЕРЕНОСА В ВЯЗКИХ ЖИДКОСТЯХ (ОБЗОР)
[Текст] : статья / Ирина Викторовна Степанова // Вестник Омского университета. - 2019. - Т. 24, № 2. - С. 51-65, DOI 10.25513/1812-3996.2019.24(2).51-65
. - ISSN 1812-3996
Перевод заглавия: SYMMETRIES OF HEAT AND MASS TRANSFER EQUATIONS IN VISCOUS FLUIDS (REVIEW)
Кл.слова (ненормированные):
теоретико-групповой анализ -- симметрии -- задача групповой классификации -- бинарная смесь -- конвекция -- тепломассообмен -- коэффициенты переноса -- symmetries -- group classification problem -- binary mixture -- convection -- heat and mass transfer -- transport coefficients
Аннотация: В статье приведен обзор результатов применения метода симметрий Ли-Овсянникова к исследованию качественных свойств уравнений тепломассообмена в вязких бинарных и / или теплопроводящих жидкостях.
The paper is devoted to description of results of classical Lie-Ovsyannikov theory application to study of equations of heat and mass transfer in viscous liquids. Group properties of equations of convective and molecular heat and mass transfer are under consideration. The author analyzed more than 120 papers and monographs be concerning to the mentioned problem.
РИНЦ
Держатели документа:
ИВМ СО РАН
Сибирский федеральный университет
Доп.точки доступа:
Степанова, Ирина Викторовна; Stepanova Irina Victorovna
Перевод заглавия: SYMMETRIES OF HEAT AND MASS TRANSFER EQUATIONS IN VISCOUS FLUIDS (REVIEW)
| УДК |
Кл.слова (ненормированные):
теоретико-групповой анализ -- симметрии -- задача групповой классификации -- бинарная смесь -- конвекция -- тепломассообмен -- коэффициенты переноса -- symmetries -- group classification problem -- binary mixture -- convection -- heat and mass transfer -- transport coefficients
Аннотация: В статье приведен обзор результатов применения метода симметрий Ли-Овсянникова к исследованию качественных свойств уравнений тепломассообмена в вязких бинарных и / или теплопроводящих жидкостях.
The paper is devoted to description of results of classical Lie-Ovsyannikov theory application to study of equations of heat and mass transfer in viscous liquids. Group properties of equations of convective and molecular heat and mass transfer are under consideration. The author analyzed more than 120 papers and monographs be concerning to the mentioned problem.
РИНЦ
Держатели документа:
ИВМ СО РАН
Сибирский федеральный университет
Доп.точки доступа:
Степанова, Ирина Викторовна; Stepanova Irina Victorovna