The bimodal distribution with some Maxwell modes for the Bryan-Piddaсk equation
Abstract
The approximate solution of Bryan-Piddack equation in the form of a bimodal distribution with the Maxwell modes that describe the motion of the gas type ''Accelerating-Packing'' is constructed . The sufficient conditions for minimization of inhomogeneous weighted residual for the model of rough spheres are obtained.
Downloads
References
Cercignani C., Lampis M. On the kinetic theory of a dense gas of rough spheres. J. Statist. Phys., 1988. --53, -- P. 655-672.
Gordevsky V. D. Explicit approximate solutions of the Boltzmann equation for the model of rough spheres // Reports of the National Academy of Sciences of Ukraine (2000), 4, P. 10-13, (Ukrainian).
Gordevskyy V. D. Approximate Billow Solutions of the Kinetic Вrуаn-Pidduck Equation -- Math. Meth. Appl. Sci., 2000. -- 23. -- P. 1121-1137.
Bryan G. H. On the Application of the Determinantal Relation to the Kinetic Theory of Polyatomic Gases // Rep. British Ass. Adv. Sci., 1894. -- Vol. 64. -- P.102-106.
Карлеман Т. Математические задачи кинетической теории газов. М. : ИИЛ, (пер. с франц.), 1960. -- 118 с.
Grad H. On the kinetic theory of racefied gases // Comm. Pure and Appl. Math., 1949. -- 2. -- № 4 -- P. 331-407.
Фридлендер О. Г. Локально-максвелловские решения уравнения Больцмана //Прикладная математика и механика, 1965. -- 29. -- № 5. -- C. 973-977.
Gordevskyy V. D. On the non-stationary Maxwellians // Math. Meth. Appl. Sci, 2004. -- 27. -- P.231-247.
Черчиньяни К. Теория и приложения уравнения Больцмана. -- М. : Мир, 1978. – 495 с.
Коган М. Н. Динамика разреженного газа. -- М. : Наука, 1967. -- 440 с.
Гордевский В. Д., Гукалов А. А. Максвелловские распределения в модели шероховатых сфер // Укр. мат. журн., 2011. -- 63. -- № 5. -- С. 629-639.
Lemesheva N.V. Bimodal Distributions in the Space of a Non-Uniform Weight// Journal of Mathematical Physics, Analysis, Geometry, 2015. -- 11. -- № 3. -- P. 267-278.
Гордевский В. Д., Гукалов А. А. ''Взаимодействие локально-максвелловских потоков в модели шероховатых сфер'' // ТМФ -- 176:2, 2013. -- C. 322-336.
Гордевский В. Д., Гукалов А. А. Взаимодействие смерчевых потоков в модели Бриана-Пиддака // Вiсник Харкiвського нацiонального унiверситету iм. В.Н. Каразiна. Cepiя "Maтeмaтикa, приклaднa мaтeмaтикa i механiка", 2011. -- № 990, Випуск 64, С. 27-41.
Copyright (c) 2015 Вестник университета, серия «Maтeмaтикa, приклaднaя мaтeмaтикa и механика»
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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).