phmathВестник Государственного университета просвещения. Серия: Физика-МатематикаBulletin of Federal State University of Education. Series: Physics and Mathematics2949-50832949-5067Federal State University of Educationphmath-366Research ArticleМАТЕМАТИКАMATHEMATICSГРАНИЧНЫЕ ЗАДАЧИ ДЛЯ ОДНОМЕРНОГО КИНЕТИЧЕСКОГО УРАВНЕНИЯ С ПОСТОЯННОЙ ЧАСТОТОЙ СТОЛКНОВЕНИЙBOUNDARY PROBLEMS FOR THE ONE-DIMENSIONAL KINETIC EQUATION WITH CONSTANT FREQUENCY OF COLLISIONSЛатышевАнатолий ВасильевичLatyshevA. .kaf-matan@mgou.ruЮшкановАлександр АлексеевичYushkanovA. .kaf-tfiz@mgou.ruМосковский государственный областной университетРоссияMoscow State Regional UniversityRussian FederationМосковский государственный областной университетРоссияMoscow State Regional UniversityRussian Federation20142001202303624Copyright © Латышев А.В., Юшканов А.А., 20232023Латышев А.В., Юшканов А.А.Latyshev A..., Yushkanov 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/366

Для одномерного линеаризованного кинетического уравнения получены аналитические решения задач о температурном скачке и слабом испарении (конденсации) в случае, когда частота столкновений молекул постоянна. Рассматривается линеаризованное одномерное кинетическое уравнение с интегралом столкновений БГК (Бхатнагар, Гросс и Крук) и диффузные граничные условия.

Absrtact. For the one-dimensional linear kinetic equations are received analytical decisions of problems about temperature jump and weak evaporation (condensation) in case when frequency of collisions of molecules is constant. The linear one-dimensional kinetic equation with integral of collisions type BGK (Bhatnagar, Gross and Krook) and diffusive boundary conditions are considered.

кинетическое уравнениечастота столкновенийзаконы сохраненияразделение переменныххарактеристическое уравнениедисперсионное уравнениедискретный и непрерывный спектры характеристического уравнениясобственные функцииграничные задачиkinetic equationfrequency of collisionspreservation lawsdivision of variablescharacteristical equationdispersion equationdiscrete and continuous spectraeigen functionsboundary problemsReferencesBugrimov A.L., Latyshev A.V., Yushkanov A.A. The kinetic onedimensional equation with frequency of collisions, affine depending on the module molecular velocity // arXiv:1403.2068v1 [math-ph] 9 Mar 2014, 20pp.Bugrimov A.L., Latyshev A.V., Yushkanov A.A. The kinetic onedimensional equation with frequency of collisions, affine depending on the module molecular velocity // arXiv:1403.2068v1 [math-ph] 9 Mar 2014, 20pp.Bugrimov A.L., Latyshev A.V., Yushkanov A.A. Boundary problems for the one-dimensional kinetic equation with frequency of collisions, affine depending on the module velocity // ArXiv:1403.5854, [math-ph] 23 Mar 2014, 30 pp.Bugrimov A.L., Latyshev A.V., Yushkanov A.A. Boundary problems for the one-dimensional kinetic equation with frequency of collisions, affine depending on the module velocity // ArXiv:1403.5854, [math-ph] 23 Mar 2014, 30 pp.Latyshev A.V., Yushkanov A.A. Kinetic equatios type Williams and their exact solutions. Monograph. M.: MGOU (Moscow State Regional University), 2004, 271 p. [russian].Latyshev A.V., Yushkanov A.A. Kinetic equatios type Williams and their exact solutions. Monograph. M.: MGOU (Moscow State Regional University), 2004, 271 p. [russian].Latyshev A.V. Application of case’ method to the solution of linear kinetic BGK equation in a problem about temperature jump // Appl. math. and mech. 1990. V. 54. Is. 4. P. 581-586. [russian].Latyshev A.V. Application of case’ method to the solution of linear kinetic BGK equation in a problem about temperature jump // Appl. math. and mech. 1990. V. 54. Is. 4. P. 581-586. [russian].Latyshev A.V., Yushkanov A.A. 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"). 1993. 6. 143-155 pp. [russian].Latyshev A.V., Yushkanov A.A. 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"). 1993. 6. 143-155 pp. [russian].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].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]. ISSN 2072-8387 ] Вестник МГОУ. Серия: Физика-Математика f 2014 / № 3Latyshev 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]. ISSN 2072-8387 ] Вестник МГОУ. Серия: Физика-Математика f 2014 / № 3Latyshev A.V., Yushkanov A.A. The Smoluchowski problem in polyatomic gases // Letters in J. of Tech. Phys. 1998. V. 24. 17. P. 8590. [russian].Latyshev A.V., Yushkanov A.A. The Smoluchowski problem in polyatomic gases // Letters in J. of Tech. Phys. 1998. V. 24. 17. P. 8590. [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. 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. Temperature jump in degenerate quantum gases with the Bogoliubov excitation energy and in the presence of the Bose-Einstein condensate, Theor. Math. Phys., 165:1 (2010), 1358-1370.Latyshev A.V., Yushkanov A.A. Temperature jump in degenerate quantum gases with the Bogoliubov excitation energy and in the presence of the Bose-Einstein condensate, Theor. Math. Phys., 165:1 (2010), 1358-1370.Latyshev A.V., Yushkanov A.A. Smoluchowski problem for electrons in metal // Theor. Math. Phys. 2005, january, V. 142. 1. С. 93-111. [russian].Latyshev A.V., Yushkanov A.A. Smoluchowski problem for electrons in metal // Theor. Math. Phys. 2005, january, V. 142. 1. С. 93-111. [russian].Latyshev A.V., Yushkanov A.A. Smoluchowski problem for metals with mirror-diffusive boundary conditions //Theor. and Math. Phys. October 2009, Volume 161, Is. 1, pp. 1403-1414.Latyshev A.V., Yushkanov A.A. Smoluchowski problem for metals with mirror-diffusive boundary conditions //Theor. and Math. Phys. October 2009, Volume 161, Is. 1, pp. 1403-1414.Latyshev A.V., Yushkanov A.A. Boundary value problems for quantum gases. Monograph M.: MGOU, 2012, 266 p.[russian].Latyshev A.V., Yushkanov A.A. Boundary value problems for quantum gases. Monograph M.: MGOU, 2012, 266 p.[russian].Cercignani С., Frezzoti A. Linearized analysis of a one-speed B.G.K. model in the case of strong condensation // Bulgarian Academy of sci. theor. appl. mech. Sofia. 1988. V. XIX. 3. 19-23 P.Cercignani С., Frezzoti A. Linearized analysis of a one-speed B.G.K. model in the case of strong condensation // Bulgarian Academy of sci. theor. appl. mech. Sofia. 1988. V. XIX. 3. 19-23 P.Latyshev A.V., Yushkanov A.A. Analytical solution of onedimensional problem about moderate strong evaporation (and condensation) in half-space // Appl. mech. and tech. physics. 1993. 1. 102-109 p. [russian].Latyshev A.V., Yushkanov A.A. Analytical solution of onedimensional problem about moderate strong evaporation (and condensation) in half-space // Appl. mech. and tech. physics. 1993. 1. 102-109 p. [russian].Vladimirov V.S., Zharinov V.V. Equations of mathematical physics. M.: Fizmatlit. 2000. 399 с. [russian].Vladimirov V.S., Zharinov V.V. Equations of mathematical physics. M.: Fizmatlit. 2000. 399 с. [russian].Gakhov F.D. Boundary value problems. M.: Nauka. 640 p.[russian].Gakhov F.D. Boundary value problems. M.: Nauka. 640 p.[russian].

The authors declare that there are no conflicts of interest present.