Global solvability of a nonlinear Boltzmann equation
Бейсызықты Больцман теңдеуiнiң барлық уақытта шешiлетiндiгi
Глобальная разрешимость нелинейного уравнения Больцмана
Akysh A.Sh.
2022E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2022#107Issue 34 - 16 pp.
In this paper, based on the splitting method scheme, the existence and uniqueness theorem on the whole time interval t ∈ [0, T), T ≤ ∞ for the full nonlinear Boltzmann equation in the nonequilibrium case is proved where the intermolecular interactions are hard-sphere molecule and central forces. Considering the existence of a bounded solution in the space C, the strict positivity of the solution to the full nonlinear Boltzmann equation is proved when the initial function is positive. On the basis of this some mathematical justification of the H−theorem of Boltzmann is shown.
Boltzmanns H−theorem , existence and uniqueness theorem on the whole time for the nonlinear Boltzmann equation , full nonlinear Boltzmann equation , positivity of the solution to the nonlinear Boltzmann equation , splitting method
Text of the article Перейти на текст статьи
Almaty, Kazakhstan
Almaty
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026