phmathВестник Государственного университета просвещения. Серия: Физика-МатематикаBulletin of Federal State University of Education. Series: Physics and Mathematics2949-50832949-5067Federal State University of Educationphmath-373Research ArticleРАЗДЕЛ I. МАТЕМАТИКАSECTION I. MATHEMATICSГРАНИЧНЫЕ ЗАДАЧИ ДЛЯ ОДНОМЕРНОГО КИНЕТИЧЕСКОГО УРАВНЕНИЯ С ЧАСТОТОЙ СТОЛКНОВЕНИЙ, ПРОПОРЦИОНАЛЬНОЙ МОДУЛЮ СКОРОСТИ МОЛЕКУЛBOUNDARY PROBLEMS FOR THE ONE-DIMENSIONAL KINETIC EQUATION WITH THE FREQUENCY OF COLLISIONS PROPORTIONAL TO THE MODULE OF VELOCITY OF MOLECULESЛатышевАнатолий ВасильевичLatyshevA. .kaf-matan@mgou.ruМосковский государственный областной университет (МГОУ)РоссияMoscow State Regional UniversityRussian Federation20142001202304728Copyright © Латышев А.В., 20232023Латышев А.В.Latyshev A...Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.physmathmgou.ru/jour/article/view/373

Для одномерного линеаризованного кинетического уравнения с частотой столкновений молекул, пропорциональной модулю скорости молекул, получены аналитические решения задач о температурном скачке и слабом испарении (конденсации). Рассматриваются диффузные граничные условия. Найдены величины скачков температуры и концентрации. Построены распределения концентрации, массовой скорости и температуры. Проделаны необходимые численные расчеты и графические исследования.

For the one-dimensional linear kinetic equation with collision frequency proportional to the module of molecular velocity, analytical solutionsof problems on temperature jump and weak evaporation (condensation) are received. Diffusively boundary conditions are considered. Quantities of jumps of temperature and concentration are found. Distributions of concentration, mass velocityand temperature are constructed. Necessary numerical calculations and graphic researches are done.

кинетическое уравнениечастота столкновенийграничные задачискачок температурыскачок числовой плотностианалитическое решениераспределение макропараметровkinetic equationfrequency of collisionsboundary problemstemperature jumpjump of numerical densityanalytical solutiondistribution of macroparametersReferencesБугримов А.Л., ЛатышевА.В., ЮшкановА.А. Кинетическое одномерноеуравнение счастотойстолкновений, аффинно зависящейот модуля скорости молекул//Вестник Московского государственного областного университета. Серия «Физика-математика». 2014. № 1, с. 3-15.Бугримов А.Л., ЛатышевА.В., ЮшкановА.А. Кинетическое одномерноеуравнение счастотойстолкновений, аффинно зависящейот модуля скорости молекул//Вестник Московского государственного областного университета. Серия «Физика-математика». 2014. № 1, с. 3-15.БугримовА.Л., ЛатышевА.В., Юшканов А.А. Граничные задачи дляодномерного уравнения с частотой столкновений, аффиннозависящейот модуля скорости молекул// Вестник Московского государственного областного университета. Серия «Физика- математика». 2014. № 2, с. 3-20.БугримовА.Л., ЛатышевА.В., Юшканов А.А. Граничные задачи дляодномерного уравнения с частотой столкновений, аффиннозависящейот модуля скорости молекул// Вестник Московского государственного областного университета. Серия «Физика- математика». 2014. № 2, с. 3-20.Латышев А.В., Юшканов А.А. Граничные задачи для одномерного кинетическог о уравнения с постоянной частотой столкновений// Вестник Московского государственного областного университета. Серия «Физика-математика». 2014. № 3, с. 3-22.Латышев А.В., Юшканов А.А. Граничные задачи для одномерного кинетическог о уравнения с постоянной частотой столкновений// Вестник Московского государственного областного университета. Серия «Физика-математика». 2014. № 3, с. 3-22.LatyshevA.V., Yushkanov A.A. 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Boundary problems for model Boltzmann equation with frequency proportional to velocity of moleculs// Izvestiya Russian Academy of Science. Ser. Mechanika, Fluid and Gas (Russian "Fluids Dynamics"). 1996. № 3. 140-153 pp. [russian].Dolgosheina E.B., Latyshev A.V., Yushkanov A.A. Analytical solution of the problem about strong evaporation (condensation)// Izvestiya Russian Academy of Science. Ser. Mechanika, Fluid and Gas (Russian "Fluids Dynamics"). 1993. № 6. 143-155 pp. [russian].Dolgosheina E.B., Latyshev A.V., Yushkanov A.A. Analytical solution of the problem about strong evaporation (condensation)// Izvestiya Russian Academy of Science. Ser. Mechanika, Fluid and Gas (Russian "Fluids Dynamics"). 1993. № 6. 143-155 pp. [russian].Cassell J.S., Williams M.M.R. An exact solution of the temperature slip problem in rarefied gases// Transport Theory and Statist. Physics, 2(1), 81-90 (1972).Cassell J.S., Williams M.M.R. An exact solution of the temperature slip problem in rarefied gases// Transport Theory and Statist. Physics, 2(1), 81-90 (1972).Latyshev A.V., Yushkanov A.A. Temperature jump and weak evaporatuion in molecular gases// J. of experim. and theor. physics. 1998. V. 114. Issue. 3(9). P. 956-971. [russian].Latyshev A.V., Yushkanov A.A. Temperature jump and weak evaporatuion in molecular gases// J. of experim. and theor. physics. 1998. V. 114. Issue. 3(9). P. 956-971. [russian].Latyshev A.V., Yushkanov A.A. The Smoluchowski problem in polyatomic gases// Letters in J. of Tech. Phys. 1998. V. 24. 17. P. 85-90. [russian].Latyshev A.V., Yushkanov A.A. The Smoluchowski problem in polyatomic gases// Letters in J. of Tech. Phys. 1998. V. 24. 17. P. 85-90. [russian].Latyshev A.V., Yushkanov A.A. Analytic solutions of boundary value problem for model kinetic equatins// Math. Models of Non-Linear Excitations, Transfer, Dynamics, and control in condensed Systems and Other Media. Edited by L.A. Uvarova and A.V. Latyshev. Kluwer Academic. New York-Moscow. 2001. P. 17-24.Latyshev A.V., Yushkanov A.A. Analytic solutions of boundary value problem for model kinetic equatins// Math. Models of Non-Linear Excitations, Transfer, Dynamics, and control in condensed Systems and Other Media. Edited by L.A. Uvarova and A.V. Latyshev. Kluwer Academic. New York-Moscow. 2001. P. 17-24.Latyshev A.V., Yushkanov A.A. Smolukhowski problem for degenerate Bose gases// Theoretical and Mathematical Physics. Springer New York. Vol. 155, 3,June, 2008, pp. 936 - 948.Latyshev A.V., Yushkanov A.A. Smolukhowski problem for degenerate Bose gases// Theoretical and Mathematical Physics. Springer New York. Vol. 155, 3,June, 2008, pp. 936 - 948.Latyshev A.V., Yushkanov A.A. Temperature jump in degenerate quantum gases in the presence of the Bose-Einstein condensate // Theor. Math. Phys. 2010. V. 162(1). P. 95-105 [russian].Latyshev A.V., Yushkanov A.A. 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The authors declare that there are no conflicts of interest present.