Rapidly relaxing solutions of the Boltzmann equation for a gas of hard spheres
Abstract
The new approximate solution for the nonlinear kinetic Boltzmann equation in the case of the model of hard spheres is found. It ensures the infinitesimality of the uniform-integral weighted discrepancy between the sides of the equation and very fast tends to zero with increasing of the time.
Downloads
References
Черчиньяни К. Теория и приложения уравнения Больцмана. М. : Мир, 1978. 495 с.
Карлеман Т. Математические задачи кинетической теории газов. М. ИЛ, 1960. 118 с.
Grad H. On the Kinetic theory of rareed gases // Comm. Pure and Appl. Math. - 1949. - V. 2, 4, P. 331-407.
Фридлендер О. Г. Локально-максвелловский решения уравнения Больцмана // Прикл. мат. и мех. 1965. Т. 29, вып. 5. С. 973 977.
Gordevskyy V. D. On the non-stationary Maxwellians // Math. Meth. Appl. Sci. (MMA 455). - 2004. - V. 27, 2. - P. 231-247.
Гордевский В. Д. Приближенное бимодальное решение уравнения Больцмана для твердых сфер // Матем. физ., анализ, геом. 1995. Т. 2, 1. С. 168176.
Гордевский В. Д. Приближенное двухпотоковое решение уравнения Больцмана // ТМФ. 1998. Т. 114, 1. С. 126136.
Gordevskyy V. D. Transitional regime between vortical states of a gas // Nonlinear Analysis: Theory, Methods and Applications (NA 3752). - 2003. - V. 53, 3-4. - P. 481-494.
Гордевський В. Д., Андрiяшева Н. В. Перехiдний режим мiж деякими локально-максвелiвськими течiями // Збiрник праць Iнституту математики НАН УкраЁни. 2007. Т. 4, 3. С. 5157
Gordevskyy V. D., Andriyasheva N. V. Interaction between "acceleratingpacking" ows in a low-temperature gas // Math. Phys., Anal., Geom. - 2009. - V. 5, 1. - P. 38-53.
Гордевський В. Д., Лемешева Н. В. Перехiдний режим мiж течiями типу "прискорення-ущiльнення" // Вiсн. Харк. нац. ун-ту iм. В. Н. Каразiна, сер. "Мат., прикл. мат, мех.". 2010. 931. C. 4958.
The copyright holder is the author.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal. (Attribution-Noncommercial-No Derivative Works licence).
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (see The Effect of Open Access).